Revealing mistake: While the guys are going for their physicals, there's a scene in which blood is drawn and you can clearly see the tube connected to the end of the syringe pumping fake blood into the container.
Factual error: A couple of times during the film, someone exclaims in horror that if this-or-that system fails, they will have to land the shuttle dead-stick (unpowered; no chance to veer off and try again). Actually, all shuttle landings are dead-stick; they are computer guided but nevertheless are unpowered, one-shot deals.
Factual error: At the end, the russian satelite is aimed straight at the moon. It couldn't have been done that way, and if they did aim at the moon, they would have had to aim to where it would be in 3 days.
Continuity mistake: During the climactic landing sequence at the end, the point of view shifts rapidly from head-on to alongside and back. Watch carefully at the first side-on view just as they're touching down; the nose of the shuttle says "Columbia". When it switches to the next head-on view, the wings say "Daedalus".
Factual error: This line of thinking is repeated twice, once by the NASA scientist and once by the Tommy Lee Jones character: "To get to the moon, you only have to go halfway - gravity will take you the rest of the way". Actually, since Earth's gravity is 6 times greater than the moon's, you would have to go 6/7ths of the way, otherwise you return to Earth.
Factual error: The X-2 only had one seat. In fact, I don't believe there were any two-seater "x-planes".
Continuity mistake: When Frank is stopped in the lobby after leaving Gerson's office if you look out the window behind Frank you see a couple walk by, a woman in a light suit and a man next to her. The shot than shifts to Gerson and back to Frank, you again see the couple walking by, within 30 seconds.
Factual error: In the shuttle landing sims, the pilot is flying, not the commander.
Continuity mistake: When the rockets blasted on the Russian satellite, it should have cleared all the debris surrounding it.
Factual error: At one point, the rotating solar power panels on IKON slam into the Shuttle, wrapping around the nose. That's bad for the astronauts! The tiles all over the Shuttle are used to absorb the tremendous heat of reentry. They are also very brittle. An impact like that would have torn them off by the hundreds, making reentry impossible.
Factual error: Before launch, Flight reads off the names of positions and then "go". During a shuttle launch, Flight reads off the names and the controller checks in with a go/no go.
Continuity mistake: In the first fifteen minuets of the film, Marcia Gay Harding's ear rings keep vanishing and reappearing.
Factual error: In the opening scene the x-plane approaches at a very high speed and abruptly makes a very sharp turn to climb straight up. Even with pressure suits this high-speed maneuver would not only kill the pilots but snap the wings off the plane as well. X-planes were carried up to high altitudes before their engines were ever lit up. Flying an x-plane at ground level just was not done.
Continuity mistake: The character Jerry, played by Donald Sutherland, snaps off one arm of his sunglasses that the doctor gave him. He uses it to assist him in fixing the door that was jammed shut. When they are suited up and coming back to Earth it shows him with the sunglasses back on from both sides of his head and the arm is on the glasses, not broken off anymore.
Other mistake: During the landing, when Jerry is getting Ethan and Roger out of the shuttle using the escape pole, the two people going out (presumably the stuntmen) look to in fact be jumping out the hatch, instead of just being pushed/thrown by Jerry.
Factual error: The superfortress has a near miss with one of the pilots who has not opened his parachute yet and is therefore still in free fall. As seen from the ground the superfortress would be just a dot in the sky, and the pilot would not yet be visible to the naked eye. Jerry says he saw it happen and he is not even using binoculars - no-one has eyesight that good.