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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: 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.
Continuity: 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: 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.
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: 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.