The trivia items below may give away important plot points.
After successfully rescuing the President, the MC-130 pilot jokingly says that "Liberty 24 is changing call signs. Liberty 24 is now Air Force One." Technically this is an actual fact. Air Force One is the name of any aircraft that is carrying the President at that time. Theoretically, if the President was in the rear seat of a fighter plane, that plane would be Air Force One. This also depends on what branch of the military the aircraft belongs. The helicopter the President flies in is designated "Marine One" as the US Marine Corps are in charge of the aircraft. If The President flies on a Navy aircraft it'd be called "Navy One". Since the United States Air Force maintains the President's plane it's designated "Air Force One".
The explicit filming of execution shot of Press Secretary Melanie Mitchel was omitted from the final cut as the director Wolfgang Petersen thought it was too intense.
Despite given multiple opportunities to leave, and despite being considered the most important person on the plane, President James Marshall is the last person to leave the plane alive.
Wolfgang Petersen's commentary and some other stories on the movie say that the original script explained that Secret Service Agent Gibbs had been a CIA Spook and had lost a lot due to the end of the Cold War so was angry at the US Government and knew the terrorists from his CIA days. It was decided it took too long to tell so it was cut from the script.