Factual error: After crashing on the asteroid, A.J. walks outside surveying the wreckage while debris is strewn out burning on the ground. This is wrong, as oxygen is needed to make something burn, and there is no oxygen on the asteroid.
Factual error: During the scene where it shows people all over the world, just before the shuttles take off, it is daylight everywhere. It would actually be dark or near dark in parts of the world.
Factual error: En route to the asteroid, the two space shuttles head to the Russian space station to refuel. To simulate gravity, the cosmonaut aboard the space station fires a few rockets to put the space station into the spin. How fast does it need to spin to reproduce Earth gravity? Assuming the space station's spoke arms (where the shuttles dock) are about 50 feet long, the answer is 8 revolutions a minute. That makes it impossible to dock - it'd be like trying to drive a car on ice-covered roads into a spinning parking garage. There's another, more fundamental, problem: the artificial gravity points in the wrong direction. Think of spinning rides at the amusement park. The spinning motion creates an artificial gravity, an effective outward-pushing force. On the space station, the spinning would tend to throw the astronauts down the station's spoke arms and back onto the shuttle. Also, the artificial gravity would taper off to nothing at the centre. But the movie's artificial gravity somehow points down, not outward, and appears to work equally well throughout the station.
Factual error: The surviving space shuttle takes off from the asteroid horizontally, like an airliner taking off from a runway. This is absurd. There is no air to provide lift for the wings, so the shuttle - with its engines providing thrust straight back - would simply trundle along the ground like a car. It doesn't use its maneuvering jets at any time, and they are far too feeble to lift the weight of the shuttle anyway. Nor do they gimbal the main engine, which would lift the shuttle vertically on an axis through the centre of the engine - they swoop gracefully into the air after a long take off. Second, they'd have to count on finding a clear length of ground on a debris strewn asteroid. Vertical takeoff, anyone?
Continuity mistake: After Sharpe and Stamper have the argument on the asteroid, Truman says they need the radio back up. When he says this, you see the countdown clock for the asteroid which is at five hours and 12 minutes. A bit later in the film, after the nuke was shut down by a technician at NASA, one of the Air Force Sergeants takes the terminal. In the background, you can see the clock again but the time on it is at six hours and 49 minutes.
Continuity mistake: At the end of the movie, after the asteroid explodes, we see Grace looking through the glass and there are reflections of NASA controllers cheering. The same shot was used earlier in the film to depict Grace looking upset at some bad news. The camera zoomed into the picture a bit, but you can still see one controller cheering.
Continuity mistake: When Harry is going to A.J's room, he bangs on the door with a golf club. You can see the white fan fall to the ground. Then when Harry walks in the fan is back on the ledge.
Continuity mistake: When in the Russian space station, AJ is in a little pit fixing something. When we see him, he has a little snow hat. The next time he has nothing on. Then back again with the little hat.
Revealing 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...
Factual error: In the Russian space station, A.J. and Lev are running to the Independence shuttle. But as the space station is falling apart, a piece of it crashes into the other end of the hallway they are currently running through. There is no way they would make it to the shuttle even with it being a few feet away; they'd get sucked out into space almost immediately.
Factual error: The shuttle crews are taking on liquid oxygen from the Russian space station. During their briefing, Truman refers to the oxygen as their fuel. Oxygen is not the fuel; oxygen is the oxidizer. The fuel is liquid hydrogen.
Factual error: It's explained in detail how the impact will cause a horrible freak tide, what it will do, and that one half of mankind will die in the nuclear winter. That's absolutely irrelevant. The asteroid is "the size of Texas," that means a quarter of a million square miles. Such an impact is called ELE (Extinction Level Event). A bigger part of the Pacific Ocean would evaporate immediately, so no matter if a wave or not. The earth would become "sterilized." So no lifeform will live long enough to die in a winter. (So it is nonsensical to compare that impact with the event 65 million years ago. It's much different).
Factual error: When A.J. starts up the Armadillo to jump the canyon, you can hear the sound of big, internal combustion engines. The Armadillo must have electric engines in order to function in the vacuum of space. Electric engines are virtually silent.
Continuity mistake: The first meteor is a direct hit on a street vendor in NY where the dog is chewing on one of his Godzilla figurines. To start with he's chewing a small Godzilla, then it cuts to the vendor tugging on it, then it cuts back and its suddenly a much larger one.
Continuity mistake: Even though the second shuttle takes off later then the first, they are neck and neck when they clear the atmosphere.
Continuity mistake: When A.J.'s Armadillo needs to break out of the space shuttle, the crew shoot up the walls of the hull of the ship. But then when they drive the Armadillo through the hull, the ship breaks apart at the seams rather than at the bullet holes.