Here's my cap:
I had a camera system, but disabled it so one thing would become obvious: whenever you enter a new animation (or not -- see edit at the bottom), the sprite assigned to the invisible platform object teleports to 0,0 for a single tick. That little number in the top left increments every time the sprite's X is less than 20 -- if you walk around for a few seconds, you'll see it go up pretty quick.
The thing is, it WON'T increment if you're testing the actual platform object's X value, meaning the problem must lie within the event setting the sprite's position to the object. It's a simple "Every tick" event, and absolutely no where else do I change the sprite's position. I'm led to believe it might be a bug or something, but I can't be sure.
EDIT: I disabled ALL the event sheets other than 1-1 and Mario and the problem persists, so you don't have to look in any others. Actually, I just disabled all the animations and it STILL happens, so the problem isn't even in changing animations. I'm stumped.