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.
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 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.
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.
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: 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.
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: 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°).
Continuity mistake: When Grace throws down Thurman because of frustration, she first grabs him by the back, but in the next shot he's facing upwards. (01:55:25)