The Communication Blackout
The movie: The debris knocked out the satellite communications for any spacecraft orbiting at 230 miles off-Earth, and above. Because of this, Kowalsky and Stone had to operate "in the blind" (a real phrase pilots and astronauts use when they can't connect with ground control).
Real life: According to Neil deGrasse Tyson, the blackout wouldn't have happened because communications satellites orbit 100 times higher than 230 miles. Maybe ground control just didn't feel like chatting with the survivors? Kowalsky does tell a lot of the same stories...