Mine has done that from day one. I pass it off as the screen unlocking itself. I do not see it as a problem.

 

This is actually a big issue with the Droid. The hinge, in fact, should not be loose. Pressing on the screen in ALL four corners should not make a clicking noise or move down inside. This means that the Droid's hinge has loosened and you should get this exchanged. However, the problem is that most Verizon Techs are in fact NOT experienced with this problem and most will either deny that it actually occurs or say that it is "normal". However, in my case, it became loose in a matter of less than one week. By week 2, it was opening itself in my jeans WAY too frequently. I decided to take affirmative action by calling Verizon and explaining my situation. They told me to bring it into a store. I decided that I did not want to do this and just kept the phone, until a new problem arose. Then my restarting occurred. I promptly called Verizon and they agreed to replace my phone. What I suggest is that you find another problem to couple it with. If worst comes to worst, the good old "phone is restarting" works. However, try to refrain from doing the latter because it ruins the chances for the people who really have restarting phones.