Wrong Plane Tickets
The reservations for two airplane tickets to Paris are made under Jennifer's name. When at NORAD McKittrick tells David he's got reservations to Paris and demands to know who he's working with.
F-16 or F-15?
The General yells "Send out the F-16s". When the footage appears it shows F-15s taking off.
DEFCON Sign Reverses?
The first time they show defcon, they take it from 5 to 4. Five is on the LEFT side, and 1 is on the right. Next time that they show this, 5 is on the RIGHT, and 1 is on the LEFT.
Galaga Goof-Up
In the scene when Matthew Broderick is in the arcade playing Galaga, you clearly see when Ally Sheedy walks up to him to ask about getting her grade changed, you see on the game screen he has 3 reserve ships. His current ship gets blown up, but then the game is over. What happened to his other two reserve ships?