What are the problems with MSR/LFTR technology? This turns out to be a hard question to answer. Since there are a large number of LFTR design options, however, it is difficult to identify a set of problems that shared all of the options. Rather we should talk about elective choices, and the problems that a MSR/LFTR designer would face if a certain option were chosen.

Protactinium would seemingly pose a problem for thorium breeding. The Protactinium nucleus is a very big target for neutrons in a LFTR core. Kirk Sorensen discussed the problems posed by Pa-233 and U-233 in MSR blanket salts:
From these cross-sections, you can see that thorium-232 has a moderate cross-section for absorption, but there’s so much of it in the blanket that it does almost all the neutron-absorbing (as we would want).

After absorbing a neutron, the Th-232 becomes Th-233, which has a monster absorption cross-section (almost 200x that of Th-232) but its half-life is so short (22 min) that it isn’t around very long to absorb a neutron.

Once it turns into Pa-233, the absorption cross-section is still over 5 times greater than the Th-232. That is one of the basic reasons why it’s so important to isolate the Pa-233 from the blanket–in order to prevent another neutron absorption. This is a key step that you just can’t do in a solid-core reactor that’s trying to “burn” thorium (and achieve a conversion ratio of > 1.0).

Finally, the Pa-233 decays to U-233 in 27 days. The U-233 has a huge cross-section, mostly for fission (531 barns) but with a lot of absorption (45 barns). Thus, uranium-233 left in the blanket will really want to gobble up blanket neutrons and cause fission. That leads to even more trouble, because that will deposit fission products in the blanket, complicating reprocessing and making the blanket “hot” with radiation from fission products.

All of these factors argue for getting protactinium of out the blanket and letting it decay to U-233 outside of the neutron flux. The U-233 can then be removed by fluorination to UF6 and adding it back to the core salt by reduction to UF4. Continuous refueling of the core means that excess reactivity in the core can be held to almost nothing, an extremely important consideration for safe operation that is very difficult to achieve in a solid-core reactor.
This problem would seem to be compounded in a single fluid LFTR, in which thorium breeding takes place in the same fluid that carries the fissionable nuclear fuel. protactinium is not easy to remove from molten salts. It turns out that it is a lot easier to wait until the Pa-233 is transformed by a gamma particle emission into U-233. There is, however, a proliferation related disadvantage to Protactinium separation in addition to the problem posed by the need to separate Protactinium out of its carrier salts. Dr Buzzo points out,
U-233 is perfectly suitable for use in a nuclear weapon, at least in theory. The thing which makes it difficult is that there would be some U-232 as well. This does not preclude the use in a weapon, but the short halflife of U-232 makes it much more radioactive and therefore difficult to handle. . . . .

it's really the U-232 which is going to make the uranium recovered less suited for weapons use.

However looking at the aspects of protactinium separation, I'm wondering if this could be a hole in the process which would allow for much lower U-232. U-232 is the daughter product of Pa-232 just as U-233 is the daugher of Pa-233. Pa-233 has a half-life of 26.9 days but Pa-232 is only 1.3 days.

This seems as if it could cause a problem. Basically if you separate the protactinium and let it decay for about eleven days, for example, you've gone through eight half-lives of Pa-232 but less one half of a halflife cycle of Pa-233. Thus you still retain about three quarters of the Pa-233 you started out with but the Pa-232 has been diminished to less than half a percent of what you started with. You could do it for even longer before you start to loose a lot of the Pa-233.

Thus, at this point you could do the process over again, removing the uranium and retaining the protactinium and you would have a very high concentration of Pa-233 and very little Pa-232, which is where the U-232 would come from. This is not very difficult and could easily be done with what is available. The result is basically an easy source of weapons grade U-233.
Therefore, according to Dr. Buzzo, it is undesirable to to separate Protactinium from its carrier salts, if you are worried about proliferation. In response to Dr. Buzzo's proliferation related concern, David LeBlanc commented,
Many of us on this site strongly favor the 2 Fluid design of having one salt with the U233 (and maybe a little thorium) and a separate salt for the thorium. The Single Fluid design however has been what most researchers have focused on since the late 1960s.

In a Single Fluid design it is much more difficult to try to skip Pa removal and still break even. The way to lower the neutron losses to Pa is to lower the average neutron flux it experiences (especially thermal neutrons). You can do this by simply having a much larger core or by having excess salt that you cycle in and out of the reactor loop. However, in a Single Fluid design, having more fuel salt means having much more fissile material to start. This is not a deal breaker but a serious impediment nonetheless.

In a 2 Fluid design we can lower losses to Pa down to almost nothing by simply increasing the volume of blanket salt. This means paying for more thorium and carrier salt but thorium is very inexpensive (the true potential cost of mass produced Flibe salt is unfortunately one of the big unknowns). For example, 1960s 2 Fluid designs had about 260 tonnes of thorium in the blanket salt versus about 70 tonnes in the later Single Fluid design.
In another thread, Dr. LeBlanc commented,
in a 2 fluid reactor you can have more blanket salt cycled in and out of your reactor to really lower the loses to Pa. Here are some numbers to give you an idea of losses (remember you can almost double the values since you often lose a second neutron to U234):

Single Fluid design with a 3 day Pa removal time, Pa losses are 0.0017 out of 2.23 neutrons

Single Fluid design WITHOUT Pa removal, Pa losses are 0.05 out of 2.23

2 Fluid design with lots of blanket salt, NO Pa removal (ORNL 1467) 0.0079 out of 2.22 (0.36%)

2 Fluid design with less blanket salt but Pa removal (ORNL 4528) 0.0002 out of 2.22.
The neutron losses for all designs noted by Dr. LeBlanc are acceptable for breeding purposes. Thus a LFTR designer has a number of potions to chose from, in creating a design that best meets breeding goals. As it turns out, according to Dr. LeBlanc, none of the options pose serious barriers to breeding goals, although one option - Single fluid design with no Pa removal - offers the most disadvantages.

There are a number of number of problems associated with core graphite in thermal MSRs. Graphite cores breeders offer huge scalability advantages, because they can be started with a small charge of fissionable material. It takes about 10 times more fissionable material to start a Fast Breeder reactor, than a graphite moderated thermal breeder requires. This makes an enormous difference in the number of reactors that can be started quickly. Well over a year ago I posted a comment on Brave New Climate,

Needless to say, IFR advocates were not pleased by this comment, but they have not been able to show that I was wrong. However, in order to wrap the thermal scalability LFTR advantage, we have to find ways to solve the graphite problems. The two major graphite problems, are
* graphite deterioration in a high neutron flux environment
* And a positive coefficient of reactivity associated with core graphite.
If we want to build a large number of LFTRs quickly then we have to find a workaround. On solution to the graphite deterioration problem is to replace the core graphite every few years. One way to accomplish this is by using graphite pebbles rather than a graphite core structure. The pebbles can be replaced as they reach a point where their deterioration become unacceptable. "Cyril R" points out,
Graphite pebbles have a lot of potential advantages. In one two fluid design, the pebbles are filled with blanket salt. This means every pebble is a barrier, and so barrier maintenance is potentially easier. However, circulating pebbles turns out to be a bit tricky, and with a lot of pebbles all containing liquid blanket salt, broken pebbles seem like a big risk in a true two fluid design. . . .

However, if solid graphite pebbles were to be used in a two fluid design like David's tube in shell, things would be easier. The pebbles wouldn't circulate, but act as fairly static moderator. The simple graphite pebbles would last longer and be easy to replace. Because pebbles have a high void fraction, the traditional MSR graphite density could not be achieved (probably at least half the graphite density).
Lars commented,
Graphite in the blanket would serve to slow the neutrons down. The slower spectrum will make all cross-sections larger so less blanket salt is required to absorb the neutrons. However, the cross-section of the fissile will grow dramatically faster than anything else - which is not good in the blanket. It means that we have to keep the u233/th232 ratio much lower to keep fission in the blanket rare. So one result is that we have to process the blanket faster to keep the u233 concentration down. I'm not sure how big an issue this is - the original 2-fluid ORNL designs were thermal and so they faced this issue and did not identify it as the reason to stop work on the 2-fluid design. But they also generally assumed they could process things at a pretty high rate.

Another effect of graphite in the blanket would be that any neutrons that hit the exterior wall would be slow so they are much easier to absorb and stop and are easier on that wall.

Another effect is that it becomes more cost effective to absorb a higher percentage of the neutrons in the blanket since the thorium in the salt is more effective at absorbing slower neutrons.

One BIG concern is that if there is a big break in the plumbing for the blanket salt you will drain the neutron absorber from the blanket. With the graphite present it will slow down and reflect many neutrons back toward the core. In normal operations the blanket salt will absorb most of them. With the blanket salt drained they will go back to the core. In other words, if you get a dramatic break in the blanket plumbing and drain the blanket salt the reactivity of the core will go up. This can not be allowed. The design would need to somehow guarantee that no matter what the reactivity of the core does not go up in any accident scenario.
David LeBlanc described his position.
your don't want graphite or other good neutron reflecting material in the blanket zone or you end up with reactivity problems if the blanket salt drains or even just gets hotter and less dense.

For the core, using graphite is always a serious option and pebbles certainly have some big advantages but they don`t really help with the core to blanket barrier issue. Even a core with graphite moderator you still need some sort of physical barrier to the separate the fuel and blanket salts (any Two Fluid or 1 and 1/2 Fluid needs barrier material). A graphite core of logs might make things a little easier because we could have a simple metal cladding wrapped around it that would need no structural strength of its own). My google tech talk also shows a method to use individual graphite logs bunched together as the barrier but too complicated to describe here.

So in general, pebbles versus logs is always going to be an interesting trade off of pros and cons. In terms of radiation damage, I still don`t know if anyone has a good idea of how long a pebble would be last. The expansion beyond original size is no longer of structural concern for the core (like it would be for logs) but it the pebble starts to crack due to expansion then we do have a big problem. ORNL seemed to be on the fence regarding this in their early studies with pebbles (which seemed always to be a Plan B that never got too deep a look).
In most cases, comments are or can be referenced back to ORNL MSR research. I could quote more of the graphite pebbles discussion which illuminates a number of problems, but this is enough to suggest that MSRs problems exist, but that solutions and work arounds are available. Each solution or work around may have its cost, so any MSR/LFTR design is going to offer a compromise. The question facing the LFTR designer is, which set of compromises works best given design goals. Because the graphite moderated LFTR is highly scalable even without a high breeding ratio, designing the LFTR to produce just one U-233 atom for every fissionable atom burned. Not only does this decrease proliferation risks, but it allows for more breeding ratio lowering compromises in the LFTR design.
There would be a set of problems for every MSR/LFTR design, but there appear to be an acceptable set of compromises for the problems we have looked at. At least some of the compromises I have reviewed, seem to have secondary benefits that are consistent with probable design goals. In the nearly 40,000 comments of the Energy from Thorium discussion section, no one single killer problem has yet popped up. This most likely means that development of various MSR designs including LFTRs will not involve serious development challenges, and we can be reasonably but not entirely certain that serious problems will not impede MSR/LFTR developmental progress.
Thus it can be assorted with reasonable certainty that the LFTR offers a potential long term solution to human energy needs, that is consistent with a high energy lifestyle, and which will not create the sort of safety, waste, proliferation and capitol cost problems associated with LWR power technology.
Update: David LeBlanc offered this comment on Nuclear Green:
"I'd chime in that you raised one issue without really further commenting on it. That being the concern of positive reactivity effects of graphite.

Without going into details, this issue is of concern only for Single Fluid Thorium breeder designs (and a solvable problem). For Two Fluid (or what's called 1 and a half Fluid) there is no such problem. As well, for Single Fluid converters that have U238 in them (i.e. the DMSR), there is also no concern here.

The last commenter had good points about salt costs. A couple things to point out, first the study he quoted assumed a huge cost of 3000$/kg for Li7 but this was just ORNL being super conservative since that was the price Light Water Reactor folks were paying at the time for tiny amounts of Li7 to help their water chemistry. Most other studies assumed 120$ a kg. This is a big unknown though but I'd also add that in most designs, even breeders but especially converters, we can get by without enriched lithium. For example NaF-BeF2 or NaF-RbF work just fine and are relatively cheap. I have a hard time convincing people of the merits of non-Li7 salts but a group in Europe has done neutronic modeling to back me up on this (not published yet)."