I've seen many reports of erratic touchscreens, and since I've dealt with a couple myself, I thought I'd share results of my research into the problem(s):
[1] While charging, screen scrolls or selects items as your hand nears the touchscreen,
OR the touchscreen becomes completely unresponsive while charging.
[Soulution]: Use an OEM charger from your phone's manufacturer. If you must use a third-party charger, power off the phone first; that strange behavior could potentially cause damage.
[2] Possessed by demons - uncontrollable random scrolling & selection of items.
[Solution] Capacitive screens can be affected by the oily film that develops with usage over time. First try cleaning the screen with a cotton cloth or swab lightly wetted with a few drops of water or rubbing alcohol. (Avoid using general cleaning products since you don't know what they contain, or why.) Caution: Be sure it is not so wet it will drip into the phone. If that doesn't fix it, try the oven method - HOW TO: fix Droid/Milestone touchscreen lack of responsiveness and Ghost Touch issues - xda-developers. My own experience (Moto Cliq MB200), 100C/212F for about 1/2 hour is OK, and it works. (Boiling point of water is too low to melt anything in the phone, but plastics may be softened, so allow it to cool 1/2 hour before moving it.)
[3] Milestone users may have a hardware problem causing effects similar to [2]
The problem with my phone(charging or not) is that there is a spot more or less at the center of the screen that has become more sensitive than the othet parts of the screen. The spot is actually visible as a clearer looking area at the center and it keeps selecting apps only from that area. Breathing on the screen also makes the spot act up, maybe that will help diagnose the problem.