Continuity mistake: When Russell boards the F/A-18, he places the photo of his kids beside the left DDI on the instrument panel, which is to the left of the number key pad, below the HUD. When he says, "Payback's a bitch..." there is an upside-down matchbook cover (with the words, "Amraam armed....is off" scribbled on it) exactly where the photo was - beside the left DDI, but then later the photo reappears. Also note that the yellow/black zebra marker behind the photo becomes a blue marker as well. (02:09:10 - 02:13:30)
Continuity mistake: When David is explaining to the President about the aliens' intentions with Earth's satellites, he draws two lines that start at the destroyer and go off straight both edging off Earth. But when he places the paper back on the desk to draw in the satellites, the left lines have risen away from the Earth. (00:41:00)
Continuity mistake: When David squeezes his dad's shoulder, after he just won chess, David has a severe bruise on the middle fingernail of his left hand, which disappears as soon as he gets back to work.
Continuity mistake: In the Oval Office, when David says, "They're using our own satellites against us," the grandfather clock is about a foot away from the doorway behind him. In the previous wideshot, when Alex appears at the doorway, the grandfather clock is farther to the right, nearer to the other curtained doorway.
Continuity mistake: When President Whitmore and the rest get to Area 51, you see David Levinson in the background. Right before they go through the doors, he has a sunglasses clip over his glasses. As they start walking down the ramp, they are still on, but right after the glass doors open, you can see for a second or two the clip is off the glasses. Then when they go for a close up of Levinson, you can see him take the clip off. (01:14:55)
Continuity mistake: After the President fights the Aliens in the fighter plane he lands to see a lot of people cheering and happy. If you look at his hair when he is walking through the long white hallway, it is messed up and not perfect. A second later, when he walks into the "Command Centre", Connie and Jasmine ask to see if their husbands are okay, if you look at the President's hair, it is now slicked back and perfect. (02:13:10)
Continuity mistake: In the scene with Steven and David in the cockpit of the alien ship, as Steven hands David the cigar his fingers are close together in the shots facing him, but are spread apart in the shots facing David. (01:52:05)