Factual error: When Mission Control talks with Challenger 2, the Spacecraft's camera feeds of the Crew are displayed up on two wall-sized TV screens. Between them is the familiar Mercator map of Earth with the ground track of a low-orbiting satellite superimposed. Challenger is nowhere near low orbit: it's out past Mars, in the Asteroid Belt. The middle screen would have a schematic of the ship's interplanetary path.
Continuity mistake: Malden enters a bar to meet Connery. Sitting on Connery's right is a white-hared guy, so Malden sits on his left. We switch to watch the TV, and when we return, Malden is now on Connery's right.
Continuity mistake: When we see Dr Bradley in the back seat of the limousine on his way to the meeting, he is wearing a white shirt and a black tie. When he arrives at the meeting room, he is now wearing a black shirt and striped tie.