Am I right in saying that this only happens on the boundary between Tiled Background and Sprites (or other objects)? It doesn't look like the tiled background is breaking up inside of itself, just the borders. I will try and fix this ASAP.
Not just at the boundary between sprites and bg tiles, no... the edges of the bg tile objects themselves are just where the problem is most visible. If you have a bg tile all on it's own you might notice that it's sort of shifting around inside it's bounding box by about 1px. At least, I have.
In the .caps I posted with the bug report (the ones that no longer work), the tiles were much smaller and you could see the entire tile shifting up and down (or left and right) much easier. It's like it can't render sub-pixel increments the same way as sprites or something so it's moving the contents to the next whole pixel. I think. I'm not super techy but that's what it appears to be doing to me.
Edit:
Hehe, conflicting reports itt... We've just teamed up to confuse the hell out of you Ash