Brief testing suggests it was my edit in version 4 that did it (i.e. it wouldn't have occurred in version 3). What I think is the problem is that I didn't consider the zoom factor of the fog when fixing the tiling, which means if the fog is at 200% zoom (as it is by default), then every time you move half the width/height of the displayed fog tile (i.e. the actual width/height of the picture), the fog jumps. If it was 300% zoom it would jump 3 times per width/height of the displayed fog. 100% zoom shouldn't have any problems.
For scrolling fogs, the jumping problem seems to go away after a while, which is unexpected. The jumping also seems to behave differently at map edges.
For the code-minded, the issue is in SpriteWindow, around lines 4780 and 4810.