I have had to replace my Droid two times. I am now on Droid #3 and it finally works as it should (minus any universal oddities of which there are few and are to be expected in a 1Gen phone).
When I exchanged the first phone, they kept the original SD card and put it into the new phone. I recommend folks not do this. It has now been determined (as far as can be determined) that the SD card had corrupted data on it which caused problems for the original phone and when it was transferred over to the second phone proceeded to cause the exact same problems with that phone. Phone number 3 has a new SD card (per tech support's suggestion) and viola! No issues.
Make sure that if you must exchange - everything is new.