I had a Motorola Droid (original) and twice (original, then replacement device) the screen would become erratic and uncontrollable. It would "sense" that the screen was being touched in some areas, open apps, and make it impossible to type. It would usually clear up after a few hours, if not over night.
Now I have the Droid Razr (got it 11/11) and this phone began doing it as well. It is not as severe, but I cannot use Swype nor make phone calls without turning the screen off.