Motorola Milestone is constantly firing touch events
There is a lengthy discussion about this on:

http://androidforums.com/droid-support-troubleshooting/87515-my-droids-touch-screen-going-crazy.html

The main point seems to relate to either oil and dirt covering the screen and/or heating up issues from dirt within internal components.

There are some suggested solutions such as carefully cleaning the screen and the speaker opening. It also seems to be strongly affected by moisture.