Continuity mistake: Jasmine's friend at the strip club shows off a sign she made. It changes design and grows creases. This is more evident in the special edition, as the scene is longer.
Continuity mistake: When the alien spaceships open the main gun above the White House we can just see the green light coming on at two people on the ground. When the camera cuts to the view of the spaceship the gun housing is almost completely open.
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 the shields of the motherships have been taken out and the fighters fire their missiles, we can see that the inflict a lot of damage to the mothership's front, but when Russell Casse blows the ship up that damage is gone. (02:00:55 - 02:24:45)
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: Aboard Air Force One, when David feels nauseous there is a telephone between his seat and his father's, whose cord gets twisted between shots, though it hasn't been touched.
Continuity mistake: At SETI, before the signal starts to beep, when the techie putts the golf ball there are many other golf balls lying about, which change position between the wideshot and close-up.
Continuity mistake: When Julius and David pull up beside the White House gate, David places the device on the Plymouth's hood to triangulate Connie's position inside. The device's position on the car's hood differs between the close-up and wideshot - note the car door.
Continuity mistake: Just after Steven and Jimmy board the Hornets, aboard Air Force One, General Grey receives a call from Norad and when the crewman hands the General the phone he sits down, but next close-up he is still standing. (00:58:35)
Continuity mistake: In the motorhome, when Troy bangs on the TV in the close-up his left hand is down as he leans on it, then next shot his left hand is up on the TV with his right, but when it cuts away it's back down again. (00:10:20)
Continuity mistake: When the spaceship is flying over New York, a police car stops. A cop steps outside and pedestrians walk past the car. A mere frame later, the people have vanished. (00:24:21)
Continuity mistake: As Smith leaves Jasmin to go to El Tore his uniform jacket's epaulettes are untucked then tucked and finally untucked again.
Continuity mistake: When David and Julius are playing chess at the park in Brooklyn, the slow decomposing styrofoam coffee cup, David's beeper, radio, removed chess pieces (not in play), etc., change position between shots, particularly in relation to the chess board.
Continuity mistake: In the Area 51 lab, after the alien is shot, when Major Mitchell rushes over to Dr. Okun's body, his head moves closer to the monitor between shots, as well as other changes. (01:32:00)
Continuity mistake: The Commander walks into the Oval Office to tell the President that the object settled into a stationary orbit, and when the silver briefcase is placed and then opened on the table things move and a paper disappears. (More visible in fullscreen)
Answer: Remember that the aliens had to interface with our satellite computer code first...David simply "reverse engineered" the code to create the virus. When it was uploaded, they didn't have enough time to combat it.