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.
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.