Hey geod,
Here's an update I did to your upload. I did a few tweaks to the title screen and I think all the random buggy behavior is removed from the first level now.
I also did the 2nd level and about half of the third level (up to the part where the spikes fall in the pink cave).
This is a game that will probably have to be gone through one frame at a time because just the slightest movement can cause a change in background sprites, even if only for a second. This leads to a lot of weird glitchy flashes if they aren't fixed manually. Like I said, I believe that level one is about 99% glitch free or better. Level 2 is probably 90% glitch free. The first half of level three is probably 80%.
I'd like to spend more time on this game, but I probably won't mess with it anymore until we at least have save states.