Initially director Wolfgang Petersen was denied access to the real-life Air Force One. A telephone call from Harrison Ford to the White House soon changed that.
Harrison Ford told Gary Oldman to actually hit him during the filming of the fight scenes.
Gary Oldman's (Ivan Korshunov) chilling performance earned him the nickname "Scary Gary" during production, however he did not stay in character between the scenes. Director Wolfgang Peterson called the filming experience 'Air Force Fun' because of how comedic and genial Oldman would be off-screen. He also said that Oldman would suddenly return to the menacing film persona like a shot. Harrison Ford has since named Oldman as his favorite on-screen nemesis.
One day during filming, two F/A-18 fighters appeared and radioed in a surprised report that the plane they'd been asked to identify was Air Force One and there were bullet holes in it. (They were actually decals). The air traffic control center in Los Angeles knew about the filming and was able to set them straight.
The lead role was written for Kevin Costner, but he was heavily committed to The Postman (1997), and suggested Harrison Ford for the part.