If only some saves are doing this, it sounds like they are corrupt. That seems weirder than the game acting as if Caps Lock was enabled.
Does teleporting, via the stones or pads, update the screen location to follow the character? Probably not.
If you are interested in narrowing down where the problem is, you could make copies of a non-working save folder and a working one, then start copying files from the working save into the non-working save until it starts to work after being loaded. Alternately, you could copy files from the non-working save folder into the working folder until it stops working. I would start testing with the data.000 file.