Character mistake: When Sharp is teaching AJ to remote detonate the bomb, he says to "lift, press, hold" the trigger device. But the actions with the hands are actually "lift, hold, press." Even AJ repeats it wrong. (02:11:00)
Suggested correction: Lift (the cover), press (the button), hold (the button). That's the sequence.
The suggested correction sequence leaves out the trigger. The original mistake entry seems to be accurate. After watching again, Harry lifts the cover off the trigger, holds the trigger, and then presses the button. Lift, hold, press.
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.
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.
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°).
Other mistake: If the meteor shower that hits NYC is the same one that destroyed the shuttle, how was so much time able to pass that all the newspapers were able to report on the shuttle before NYC got hit?
Suggested correction: Good question. Nobody says that it's the "same" shower though. All of them come from the bigger rock, and they are coming in intervals. So it could very well be some time had passed between showers. Also, the meteorites that hit the shuttle were much smaller and probably burned up in the atmosphere before bigger ones followed.
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.
Factual error: Both shuttles are approaching the Russian space station with their main engines on, without atmosphere that would not be needed.
Other mistake: Adding on to the idea of the shuttles flying too close together, at a couple points the ejected shuttles from one booster appear to fly directly into the flight path of the tailing shuttle. While is certainly possible the second shuttle could maneuver to avoid the collision, it further demonstrates the absurdities of launching the two craft in such close proximity.