Revealing mistake: Early in the film Gene Hackman tests a rocket-powered backpack outside the space station. He slowly spins sideways through a complete circle, but instead of each side of his body being lit up in turn as it's pointed towards the sun, the light stays constant throughout the maneuver, showing that the makers just took a photo of Hackman and rotated it.
Revealing mistake: When the lift body first separates from the orbiter you can see the support wires for the orbiter hanging below (scene must have been filmed upside down).