I have found in using my Motorola Droid that it is vitally important to keep the touch screen and/or the clear plastic touch screen cover clean, without scratches, grease, or dirt. When my Droid was new, I was able to use it quite a bit with the same screen cover for quite a while, but recently I have gone through two plastic protection covers in order to keep the Droid responsive.
I am wondering if there is build up somewhere, so I removed the most recent cover and cleaned the glass surface. That helped, but the newest cover has gotten scratched in the first two weeks of use; I have one left before I have to get some more. Before replacing the most recent one, the Droid wasn't responding, especially to touches on the bottom left of the touch screen.
It's real important to keep the screen clear and viewable at all times.