Minecraft wiki entry for Infdev_20100327_to_Beta_1.7.3, associated text: Noise is sampled only every four blocks and linearly interpolated in between. This is why when 12,550,824 is affected by the bug, it reaches out three more blocks to 12,550,821.
Each noise generator picks a random offset in [0, 256) to add to its input. This usually moves the boundary under 12,550,824, starting the Far Lands at 12,550,821. With a few seeds, it might not, putting the start at 12,550,825. Very rarely, if the boundary is just barely within 12,550,824, the first couple blocks of the Far Lands might look somewhat normal. The southern and eastern Far Lands do this independently of one another. At the negative end, the Far Lands always start at block coordinate −12,550,825, with the positive edge of those blocks at −12,550,824.
The two sets of noise generators (low noise and high noise) are blended together based on another noise generator (selector noise). This is responsible for relatively smooth alternation between two sets of tunnels or plains. Occasionally, one of the noise generators starts generating the Far Lands before the other because it uses a different offset, producing an incongruous boundary.