Factual error: David is in New York playing chess and then goes to the station riding his bike through the office. When he goes past the vending machines, the water machine is Arrowhead branded, which is a California / west coast water brand - not on the east coast. (00:07:00)
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.
Continuity mistake: Jasmine's friend at the strip club shows off a sign she made. It changes design and grows creases. This is more evident in the special edition, as the scene is longer.
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.