Kind of wierd but here are some thoughts. You could be snapping to your guides. Check the View menu and see if this is enabled or disabled.
You could also be snapping. or not, to the document grid - depending on the number of divisions you've set on your rulers. You could try disabling or enabling and see what happens.
You might also check to see if layout adjustment is enabled, and what the settings are, or disabled in the Layout menu. If enabled, try disabling.
If, by any chance, you're wrapping to a graphic and you made any changes to the graphic, that'll make the text box move.
Since it happens on one doc and not another, try opening the one that was ok and check the settings. Then compare to a problem doc. There's a preference called Compositon, but that should effect all docs.
The slow redraws has me. That's usually a memory thing. If you're on a mac, you can trash the preferences - User/Library/Preferences/Adobe indesign. I don't know how to trash prefs in Windows.
Last, if you happen to be using a notebok with a trackpad, try a mouse.