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.
Factual error: We're given to believe that the mission control in NYC is under the AT&T building on Thomas Street. The scene showing the destruction in Manhattan does not go south enough to have had any impact on this building, and the subway tunnels used to escape after mission control is damaged are nowhere near the Hudson river. The illusion given by the movie is that water sloshes up against the tunnel walls.
Factual error: All movies make the same mistake when depicting nuclear explosions in a vacuum. You get a large fireball which would melt but not destroy the asteroid. Pressure waves are generated only in an atmosphere.