Impressive progress has been made, and inflation dispersion among euro area countries has broadly stabilised at a relatively low level since the launch of the single currency. To give you an example: the unweighted standard deviation of annual inflation rates stood at around 6 percentage points in the 1990s, and has broadly stabilised at around 1 percentage point since 1999.
This dispersion level is similar to that of the 14 US Metropolitan Statistical Areas (MSAs) which also stood at 1 % on average over the same period, but somewhat higher than for the four US census regions. Although such comparisons are subject to some well-known caveats, I would argue that inflation dispersion in the euro area has not been high by international standards.