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)
Factual error: When the nuclear bomb is released in Houston, the shot shows an interstate sign with South Houston as the control city. The only interstate running south of Houston is I-45, and Galveston is the control city on all its signs. (01:35:55)
Continuity mistake: The airplanes they are flying have 4 missiles, yet at the final air combat the President fires 5 missiles: the first missile hits ship with the shield on, the second and third hit the ship directly, the fourth kills a fighter alien craft, and the fifth shoots at the green light from the main ship. (02:12:15)
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)
Factual error: For anyone who is in the Air Force or has taken the time to go inside of an E-3 AWACS at an airshow you will note that the AWACS in the movie looks nothing like that of the real life version. There is no position in the back that they sit across from each other sideways as were the non pilots in the scene that the flame engulfed. The only crew that sits like that is the Navigator and Flight Engineer, but these two actors were clearly too far back for that. (00:17:40)
Factual error: When they show the Israeli Air Force with the Arabs, they show Israeli F/A-18s. The problem is that the Israelis do not own or operate any US Navy equipment - only equipment such as F-16s. (01:41:45)
Continuity mistake: At the beginning of the film, when the President is being briefed by his members of staff, there is a General wearing a blue uniform sitting by the left armrest of the couch, with his back all the way back touching the backrest. In the next shot, still by the left armrest, he is now sitting farther forward at the edge of the couch. (00:12:55)
Continuity mistake: After their daughter leaves the room, when the President tries to lie to the First Lady about her condition, her hand is touching his face in the shot facing her. In the next shot facing him, her hand is down holding his hand, but when it cuts away her hand is back up touching her husband's face.