Other mistake: A.J. gets dirt on his face although he is covered by an astronaut's suit.
Other mistake: There's grass on the edge of the cliff when the Armadillo finally lands - look just under the Armadillo while the astronaut's pulling himself up the road. Considering this is an airless, waterless asteroid, it doesn't really fit...
Other mistake: In the sequence where they are disarming the bomb. When the clock gets down to 00:24, the picture is reversed (the split second shot when they pull the clock out of the bomb). (01:48:35)
Other mistake: In the scene where the asteroids are hitting New York, there is an exterior shot of one of them hitting the South end of Grand Central Terminal. Another shot goes by and the film cuts to the main area inside the station, which is close to where the first asteroid hit. There is not one hint of damage, or any discernible reaction from the people inside from the first impact. (00:08:20)
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.
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.
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.