The taxi passenger who sits there for the whole film is Howard Jarvis, the man who co-created California's property tax reduction Proposition 13.
Hey, It's That Voice!: The Red Zone-White Zone people on the public address system at LAX were played by the people who actually recorded the public address announcements at LAX.
The little girl who likes her coffee black (like her men) was the voice of Penny in Disney's The Rescuers
Money, Dear Boy: Kareem Abdul-Jabbar's salary paid for an expensive rug he wished to purchase.
Playing with Character Type: It's surprising to think of it now, but Nielsen's role in the film was based entirely upon playing his established persona of studly, stoic heroes for laughs rather than drama. The gambit was so successful that the term Leslie Nielsen Syndrome came into existence.
Throw It In: Stewardess Randy was supposed to tell the disembarking passengers things like "Watch your step!" and "Be careful!" as they stepped onto the emergency exit slide. However, in an early take, actress Lorna Patterson unexpectedly got all the passengers to crack up by offering each of them a cheery, "Thank you for flying TransAmerican! Have a nice day!" The script was changed accordingly.
Leslie Nielsen Syndrome: This was the film that launched Nielsen's comedy career. Interestingly, this seems to be intentional. The filmmakers deliberately cast serious actors instead of comedians, thus most of the humor was delivered completely deadpan. And it works!
Pete Rose was the original choice of sports-star casting (per DVD commentary). What are the odds?
David Letterman auditioned for the role of Ted. Jerry Zucker brought the audition tape on Late Night once as a prank.
The newspaper boy who "Chews off own foot" was one of the Zucker's nephews. The DVD extras say the uncle called and asked for his school picture. He gave it to his uncle, not knowing why, only to see it in the movie later.
The aircraft that's the titular star of this film is a Boeing 707, the first sucessful commercial jet airliner not to break in half in mid-air. The "TA" logo on its tail is almost certainly a reference to TransAmerica, the company that owned Paramount at the time this was filmed. (There was also a Real Life airline company called TransAmerica Airlines, which was owned by the same TransAmerica corporation that owned Paramount; but their logo looked nothing like the "TA" tail logo shown in this movie.)
Transamerica actually owned United Artists until they sold them to MGM after the Heaven's Gate debacle; Paramount was owned by a company called Gulf+Western, which became Paramount Communications later on and was eventually acquired by Viacom.
The surfing nun on the cover of "Nun's Life" was actually Jim Zucker.
The radio station was "WZAZ" as a reference to Zucker, Abrahams, and Zucker (ZAZ), the movie's producers.
Special effects wizard Rob Bottin did Dr. Rumack's nose growing scene when he lies to the passengers, he was uncredited, he later used the same technique for the werewolf transformations in The Howling.