The distance traveled by the American and Chinese ICBM's in the final attack changes between shots.
The villain's ship is named the Su-Maru, a name which is used several times in the film. When the ship explodes the name Argonautica is on the bow; that was the name used in the film the stock footage was lifted from.
The Nuclear Football is not an actual means of launching nuclear weapons. Rather, it contains the U.S. nuclear war strategy as outlined in the Single Integrated Operational Plan. The Football's true function is to allow the President to have the capability to decide upon a nuclear option in the event of a crisis. Furthermore, in the event that the President is incapacitated, or if his Nuclear Football is compromised in any way, the Vice President also has a Nuclear Football.
NORAD does not control the U.S. nuclear arsenal. Instead, this responsibility lies with the Air Combat Command.
The Presidential limousine seen in the opening credits has a "TCP" code on the front bumper. Those are used for "charter-party carriers" (rental or hire firms) in California and would not appear on the President's car.
US secret service agents don't carry the football as seen in the film. In real life, it is carried by a military officer.