I assume this only happens with ID and not Word and the like. If it's all, I are you using a mouse and not a trackpad on a notebook? If using a trackpad, try a mouse and see if the problems goes away. If you're using a trackpad, try wiping off with a clean dry cloth and possibly trashing its prefs. If using a mouse try resetting its prefs.
I always sound like a broken record, but try trashing ID preferences while ID is off. User/Library/Preferences/com.adobe.InDesign.plist. This never hurts.
Does this happen with ALL text boxes with all fonts and things like paragraph styles? If it's just some it could be caused by something like a corrupted font cache or style, but it's not likely.
It's really wierd that it's happening to you and your boss. That's why I inquired about certain fonts, styles, etc. Especially note anything brought in wrom another app like Word or Excel.
Using OSX 10.3.9 on a G4