Continuity mistake: In two spots in the movie, first with Thornton and the second time with both Thornton and Cusack they stood on the runway over the threshold markings and waited for a landing aircraft so they could feel the strength of a wake turbulence. On final approach the pilot would have seen him/them on the runway and called a missed approach and execute a go around. You just don't land when there is an obstruction on the runway, it makes a hell of a mess of the undercarriage...
Continuity mistake: The movie seems to make a big show about the controller (Thornton and Cusack) guiding aircraft within a couple hundred feet of each other. If the movie followed actual FAA rules of aircraft separation (I believe it's a half mile vertical and two miles horizontal or so, but certainly farther than was constantly depicted), then both of them would have been suspended or fired several times over before the end of the movie. And that isn't something that would be up to their supervisors.
Continuity mistake: When Cusack is in bed with Thornton's wife, her nipple is covered in half of the shots from the side of the bed, and exposed in the other half.
Factual error: When Nick returns as a controller, he is working traffic and a conflict alarm for two aircraft on the same trajectory sounds that indicates a mid-air collision is imminent. Another controller has to jump in and order the two aircraft to change headings to avoid a crash. In the following shot, it shows the two aircraft nearly collide and the pilots look shocked. However, all aircraft have a system called TCAS or the Traffic Collision Avoidance System which notifies pilots of an incoming conflict with another aircraft. It then orders a resolution advisory such as an emergency descent or climb. Therefore, commercial pilots would have neither been unprepared for this event, nor surprised.
Factual error: Billy Bob Thornton is new at the air traffic facility, yet he plugs in and immediately begins working airplanes. Under no circumstances would he be able to do that without having someone train him first (even if he was a controller at that facility at a prior time). Each facility has its own approaches, restrictions, etc.
Continuity mistake: At the beginning of the movie Cusack and Blanchett are having sex. Afterwards Blanchett gets dressed to leave to talk to a teacher of their son and she buttons her blouse wrong. In the next shot however the blouse is buttoned correctly.