Other mistake: When the US Military is deploying a nuclear bomb against the alien attacker over Houston, you see them fire the nuke and then the B-2 breaks left, but on the screen you can see the B-2 breaking right.
Revealing mistake: When the Welcome Wagon is being shot down you can see an explosion starting inside the last helicopter before it is even being hit.
Other mistake: When David asks Major Mitchell if he can shoot the soda can, Major Mitchell has to ask a nearby sergeant for his sidearm, despite already having one on him when he shot the alien earlier.
Suggested correction: He probably shot his own gun empty or nearly empty, so he removed the magazine. They fired at least 10 shots at the alien, and he planted another 3 in it up close.