Continuity mistake: When AJ bumps into Bear his shirt is very dirty on his right side, but as he runs up the stairs it is much cleaner and has a sweat mark around the neck line. Next shot on the tower and the sweat is not in the same pattern. After he slides down the cable the dirt is in a different pattern again. (00:14:10 - 00:15:00)
Revealing mistake: When Ben Affleck riddles the shuttle's fuselage with the bullets from armadillo's gatling and then rams it to get outside, it can be seen that the side wall of the ship is paper thin. Now, I know titanium is a sturdy stuff but don't believe such a flimsy construction would be enough to stand the ordeal of a space flight with gravity loads during the start, escaping/entering the atmosphere and pressure difference in the vacuum of space.
Continuity mistake: When Harry goes into A.J.'s room, he gets mad and sticks the end of a putter golf club at A.J.'s throat. The next scene the club changes and is not a putter anymore.
Deliberate mistake: When the bomb is going to be remote detonated, on the inside lid of the briefcase, the remote destruct warning says that upon activation, the warhead will detonate in T minus 10 minutes. When the countdown begins on the bomb however, it is only for 6 minutes.
Continuity mistake: When they are boarding the shuttles, Harry and AJ have a brief chat and they get onto to bridge last. But somehow Harry manages to get in front of Rockhound and Max, and AJ manages to get in front of Oscar and Bear.
Continuity mistake: After Harry catches AJ in bed with Grace, AJ runs out of the room. Cut to the next camera angle taken from outside as AJ leaves - and he has a pair of boots tied together around his neck. They were not there in the previous shot. (00:13:00)
Audio problem: When Freedom shuttle is being destroyed by the asteroid field, you can hear Harry say, "Sharp, what the hell is that? Is that the Independence?" but you can tell by Bruce Willis' mouth that he isn't saying any of those words.
Continuity mistake: When the team meets the flight crews for the shuttles, there are two munitions specialists - Gruber and another astronaut. We see this other astronaut board the shuttle, then he's never seen again, not even his body.
Continuity mistake: The first shuttle takes off some time before the second. Nevertheless we see a picture of both shuttles in the air shortly after they clear the towers.
Factual error: When landing back on Earth, the Colonel says "100% flaps." Flap positions are graduated in°, with the extreme position being full flaps (40 to 50°).
Factual error: During the opening shot of the shuttle Atlantis in the satellite repair scenes, its cargo bay doors are closed. Standard procedure for orbiting shuttles was to keep its cargo doors open, for a variety of reasons, not the least of which is that the airlock is located within the cargo bay. The astronaut isn't tethered but using an MMU, but still would have to enter and exit through the cargo bay airlock, meaning if the doors where closed, if there were an emergency he'd have to wait for someone to open them before he could get back in.
Continuity mistake: Near the end of the film when Sharp says "Houston, we're coming home." We see Bear looking out at the Asteroid passing the Earth yet in the next shot he is strapped to his chair saying "You Harry, you the man". (02:19:55)
Other mistake: When the first shuttle has crashed, you can see that one of the characters (I think it was Liv Tyler's fiancé) has torn gloves. That would decompress his spacesuit and he'd suffocate.
Character mistake: During the scene when AJ is yelling out for any other survivors in his crashed shuttle, we hear Lev calling "A.J.", but with no Russian accent. Then Lev gets his accent back when he says "I'm here." (01:28:10)
Audio problem: During the sling shot around the moon we hear a sound in more or less every shot of jet engines being revved up. They couldn't rev the engines up several times - it's not like such engines have gears.
Audio problem: When the Russian space station is on fire, and the crews are running out, you can hear Harry say, "Where's the rest of the team?" but his lips don't move.
Continuity mistake: As Harry's crew is about to start drilling, Rockhound analyzes the surface. The drilling head is already bellow the asteroids surface. When the camera pans back to Rockhound the drill head can still be seen slowly turning on the upper right corner.
Factual error: The military sends a signal to the drilling team's nuke, arming it and triggering a countdown. A sudden rush to disarm the warhead ensues, with the NASA team on Earth temporarily breaking the uplink and stopping the detonation countdown. However, modern nuclear weapons do not require a "constant uplink" to detonate. Once the signal is sent and the nuke is armed, the signal can be cut or interrupted and the nuke will continue counting down.
Revealing mistake: When AJ drives through the wall in the spaceship wreckage, the material flaps about in a very un-metallic way.
Factual error: The nuke is provided by the military, not NASA. There is no reason why the NASA guys should have any access to the bomb. So, the idea of some random technician at Mission Control punching in a few numbers on a keyboard and somehow shutting off the bomb makes absolutely no sense.
Answer: If you look at the deleted scenes on the special edition DVD, you will see a deleted scene in which A.J. asks what they needed a gun for, and Max explains that it's for debris elimination, in order to take out small rocks in the way.