My wife and I both have pre-order SIIIs...mine is the 32gb Blue and hers is the 32gb white. Out of nowhere about a week ago my phone battery started not charging worth a crap. I was on it at work when it went to the red, hooked up the charger that came with it and kept texting. After a little bit the phone went black, the battery had died on the charger. Her and I traded batteries, and things have seemed ok. We called VZ and they are sending us a new battery.
Tonight it did the same thing. The battery status was red and the lock screen showed 6% and charging. I started playing MyRailroad and a half hour later the phone went black again, battery was dead.