Factual error: After crashing on the asteroid, A.J. walks outside surveying the wreckage while debris is strewn out burning on the ground. This is wrong, as oxygen is needed to make something burn, and there is no oxygen on the asteroid.
Continuity mistake: After Sharpe and Stamper have the argument on the asteroid, Truman says they need the radio back up. When he says this, you see the countdown clock for the asteroid which is at five hours and 12 minutes. A bit later in the film, after the nuke was shut down by a technician at NASA, one of the Air Force Sergeants takes the terminal. In the background, you can see the clock again but the time on it is at six hours and 49 minutes.
Continuity mistake: There are two crews boarding their spacecraft, called "Freedom" and "Independence." They are mounting a ramp and when on top, there is a crew member who directs the two different crews toward their ship: "Independence on the left, Freedom on the right." We even see the ships (in their initial launch phases) right next to each other - you can see one right next to the other as they launch. Then, once they're airborne, we see a long shot of the two bright engines, miles apart.
Continuity mistake: During the scene where AJ is playing with cookies on Grace's stomach on the last night before the launch, the car behind them alternately appears and disappears as well as moves around. Best example - wide shot shows them well behind the car, then in a shot of Grace her head's right by the tyre.
Continuity mistake: Just after Harry says "prepare the world for bad news," air raid sirens start. There's a panning down shot of some air raid speakers next to a Coca-Cola ad, with a truck parked in front of it. The angle then changes to a shot down the street (same street, same speakers, same Coca-Cola ad), except the truck isn't in front of the ad any more.
Continuity mistake: When Harry is golfing off of the oil rig, the holes on the golf ball are spaced about a yard away. In the next shot, before he hits it, the holes are right together. It also goes from saying just "Srixon" to "3 Srixon," then the lettering gets angled, then he finally hits it.