Revealing mistake: In the very beginning when we are flying over the dead town in a helicopter, look closely at one of the very first shots of the "empty" city. On one of the left side streets you can see a car driving down the road. It's not a character mistake because she is looking hard out the window and should have spotted the moving car.
Visible crew/equipment: Very close to the beginning of the film, when they first land the helicopter in the abandoned city, there is an alligator on the steps of a bank. A few seconds later when a zombie comes out of the bank and the alligator runs down the steps, you can see a red band covering his mouth (that wasn't there before) to prevent him from biting the actor.