Yes, it happens to a lot of people. Verizon/Moto were giving out three free battery doors (why 3 at a time I have no clue) and ran out quicker than a bakery in a town full of fat people.
For those of us that didn't get on that train before it left the station, there are a couple different fixes. One of them involves slightly bending the metal part at the top (just under the camera section) up ever so slightly...or there is what I do, which is put a business card folded in half under the battery which makes it solid as a rock.
fix battery door droid - Google Search