The lady in the movie that "paints" her face with lipstick due to the turbulence of the plane is really one of the director's moms, Charlotte Zucker. In fact, he has included her in all of his movies. In "The Naked Gun", she was the villain's secretary who wore the watch, grabbed the gun from her desk and tried to kill Pap Smear. She also appeared in his movie "Ghost" as a bank teller.
The rather large pair that come into view during a scene where the plane's passengers are panicking belong to Kitten Natividad, best known for her roles in the 1970s sexploitation movies of Russ Meyer, like "Beneath the Valley of the Ultra Vixens."
Jill Whelan plays the sick girl, who was more well known as Gavin MacLeod's daughter on "Love Boat". Her mother was played by Joyce Bulifant, who played Gavin MacLeod's wife in "The Mary Tyler More Show".
The passenger who is left in the cab for the whole movie is Howard Jarvis. It's funny because Mr. Jarvis was very outspoken against increased public taxation. Here, the costs in the TAX-i are mounting throughout the entire film!
The name of the airline featured in the movie is Trans American (written on the side of the plane and, I believe, spoken once or twice). This is a parody of a now defunct airline in the eighties, Pan American. Pan American was often referred to by a shortened version - PanAm. The parody is that when you shorten the fictional airline the same way, it reads TransAm.
One visitor speculates that the inspiration for the airline name "Trans American" may also have come from a mafia associated racing information distribution service known as "Trans-American". You can read more about that here.
Airplane, or more importantly "I just want to tell you both 'good luck' we're all counting on you" was recently immortalized in the Star Wars episode of the Family Guy. Leslie Nielsen did his own voice.
The little boy in the spinning newspaper with the headline 'Boy Trapped In Refrigerator - Eats Own Foot' is producer Howard Koch's nine year old grandson Billy. He wasn't told his photo was going to be used in the movie and was quite stunned when he first saw it at the premiere.
An often-missed joke in the film occurs in the scene where a lackey from the airport is sent to pick up Rex Kramer. Kramer comes downstairs (oblivious to the mauling his pet dog is dealing out). We clearly see him straightening his tie in the mirror. There's a brief cut to show the dog-attack before we cut back to Rex Kramer's image in the mirror. The joke is that what *should* be his reflection steps out of the mirror into the hallway. Ingenious visual humour. Watch the scene in question and you'll get a much clearer impression of what I'm trying to describe.
The sentence "I just want to wish you both good luck, we're all counting on you", as repeatedly spoken by Leslie Nielsen in "Airplane", is also featured in "Scary Movie 3" in which Nielsen plays the president of the USA.