That's an odd issue, I haven't heard of this one before, and Google's not bringing up anything relevant either.
The only thing I can think of related to your battery drain issue shouldn't affect anything else. Are you using the included Social Networking widget for facebook? It is known to cause excessive battery drain because it syncs too often. It's going to be fixed in an update, but for now the only option is to use Facebook's own app instead of the Motorola widget. If you have other apps that are syncing, check how often they sync.
I suppose it's possible that one of the apps you downloaded could have affected system stability in that way. In which case a hard reset is probably the only thing that will fix it. You could check the comments section in the market of the apps you've downloaded to see if others have reported similar problems with a specific app. That will at least help you narrow down the cause.
Obviously, you probably don't want to do a hard reset, as it's a real hassle. While Verizon's support tends to be good, this doesn't seem like a common problem, so this might not be the right avenue for solving your issue. I would suggest signing up on the official Motorola Community Forum, here: https://supportforums.motorola.com/community/google-android/droid2?view=discussions Motorola has staff monitoring the forum, and they're especially savvy at solving problems. When they can't help you immediately, they'll often flag an engineer for assistance. And if all else fails and you have to swap your phone with Verizon for another, the Motorola guys will also file a bug report to ensure the problem gets fixed with other units.
