Factual error: In the beginning of the movie, where the astronaut is working on the satellite during an EVA, it shows the satellite far apart from the space shuttle. Also, the shuttle's bay doors were open and facing the open void of space. This is a factual error, because when NASA sends a crew to fix a satellite in space, they flip the shuttle so the bottom faces space and the windows face the Earth. The satellite is attached to the Canada Arm and the astronauts are able to service is with ease, and not having to fear shards of a giant asteroid or other space debris.
Factual error: In the Paris meteor scene, the POV is from the walkway of Notre Dame cathedral, with a very famous gargoyle in the RH side of the frame. From that POV, the Eiffel tower is visible, but the L'Hôtel national des Invalides (Napoleon's Tomb, the gold-domed building in the foreground) is in the wrong location. To show both of those structures in those positions, Notre Dame would have be located about a mile southwest of its actual location.
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°).
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.
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.