Things look hairy for a moment there, but the plane manages to take off just as the guards are about to get in front of it, and the Americans are free. USA! USA!
Actually, that should be: "CANADA! CANADA!" The movie makes it seem like it was all the CIA's idea, but Canada was responsible for at least 90 percent of the operation, and that's according to President Jimmy Carter. Ken Taylor, the Canadian diplomat who risked his neck by hiding the Americans and going out to gather intelligence, called the CIA a "junior partner" in the rescue.
"... for politely shutting up as we steal all the credit."
Also, that tense scene at the airport? Never happened. According to Mendez, the escape went off "without a hitch." In the movie, the CIA calls off the mission at the last minute and cancels the plane tickets, presumably because Affleck accidentally slipped into a Boston accent. In reality, Canada responsibly bought the plane tickets well ahead of time, and the group just walked through the airport and left with their fake storyboards and real '70s mustaches.
Apparently the fake movie was half sci-fi, half porno.