The shuttle used in the film is clearly established as "Atlantis", however, stock footage of the shuttle "Discovery" is shown during liftoff.
In the flight sequence at the beginning of the movie, Carpenter and McKendrick are shown taking off in an F-16 Falcon, but in the subsequent flight sequences they are shown in an F-14 Tomcat.
The rate of fall of the station does not depend on its mass, so getting the space shuttle off the station is not relevent. Besides, if getting the space shuttle off the station would have made a difference, just push it 1 mm away.
Wires visible during several space-walk scenes.