Other mistake: Adding on to the idea of the shuttles flying too close together, at a couple points the ejected shuttles from one booster appear to fly directly into the flight path of the tailing shuttle. While is certainly possible the second shuttle could maneuver to avoid the collision, it further demonstrates the absurdities of launching the two craft in such close proximity.
Factual error: During the opening shot of the shuttle Atlantis in the satellite repair scenes, its cargo bay doors are closed. Standard procedure for orbiting shuttles was to keep its cargo doors open, for a variety of reasons, not the least of which is that the airlock is located within the cargo bay. The astronaut isn't tethered but using an MMU, but still would have to enter and exit through the cargo bay airlock, meaning if the doors where closed, if there were an emergency he'd have to wait for someone to open them before he could get back in.
Factual error: When landing back on Earth, the Colonel says "100% flaps." Flap positions are graduated in°, with the extreme position being full flaps (40 to 50°).