Continuity mistake: Near the end of the film as the shields come down, the jets start firing missiles at the ship. There is a shot of Randy Quaid's son walking through the control room at Area 51. Notice in the background, the lights are blinking on and off. The alien ship hasn't fired it's main weapon yet. Once it does they show the lights flickering off and on in the control room. These scenes are several minutes apart.
Continuity mistake: When the aliens arrive in New York City and start to come over the city we see a man selling candy who turns around to see the spacecraft overhead. When the scene changes we see the another man turning around and colliding with a women, and the background sky has no spacecraft in it. (00:22:40)
Continuity mistake: After President Whitmore comments to General Grey that the pilots look young and nervous, when Major Mitchell speaks into the mic and asks for all flight crews to report to their designated areas, the President climbs up onto the truck behind Mitchell. Next shot though, he is only just now walking toward the truck and then climbs up. (01:55:10)
Continuity mistake: In the diner, when the alien destroyer is about to pass overhead, things begin to shake as Russell sits at the counter and the three guys are at the table. In the close-up of the table, the salt and pepper shakers appear near the coffee cup, the Diet Coke disappears and everything changes position - having nothing to due with the table shaking.
Continuity mistake: As Smith leaves Jasmin to go to El Tore his uniform jacket's epaulettes are untucked then tucked and finally untucked again.