Carlo Kitzlinger, who played the captain of the plane, is actually a real pilot. He flew for Lufthansa Airlines for many years. He assisted Joseph Gordon-Levitt with becoming a pilot for the role.
This was not filmed on a set or with set pieces, rather it was filmed on a real plane that the production bought.
The film's title alludes to squawk code 7500. In the event of a hijacking, the pilot inputs ("squawks") the code into the transponder, an onboard electronic device used to identify the aircraft on air traffic control (ATC) radar monitoring systems. Squawk code 7500 silently alerts ATC of the situation without the hijacker's knowledge.
The director wanted a hyper realistic atmosphere to the film, so rather than directing his actors on technical details like where to sit, stand, or move for the best shot or lighting, he allowed them to improvise. Joseph Gordon-Levitt said it was brutal and challenging at times, but that it let him truly immerse himself in his character.
7500 wasn't shot like a typical movie, which usually involves tackling a series of shots and scenes each day. Instead, Vollrath's methodology had his cinematographer keeping the camera rolling for up to an hour for a single take, and the editing process involved chopping up and putting together chunks of 40-60 minute material.