Other mistake: When Will Smith checks into the hotel and his credit cards are invalid, we see that the time is 5:38 and it is daylight outside. The only problem with this is that it is supposed to be around December given all the Christmas decorations. It would be dark then in the Baltimore, not soaked with daylight.
Other mistake: At the taxi cab chase at the end, you can notice when the car is a real one and when it's CGI. Note how the real car has scratches and other things on the front of it, but the CGI car, if you look closely, has almost no imperfections, and even if it does have some, it doesn't match the real car one bit. You can see these things when the car drives off his mouth or when you see Godzilla running behind.
Other mistake: When the main characters are in the motel and they hear the moth flying outside the window, Stu, the creepy deputy with the glasses, picks up a shot gun and racks a round into the chamber. In the next shot of all of people firing at the moth through the window, Stu is now holding his revolver and fires with it. When he runs of out ammo with the revolver he picks up the shotgun again and before firing racks the pump again. Since he already did that the gun should have ejected the unfired shell that was already in the chamber from earlier, but no shell is ejected.