Trivia: The baseball blooper reel shows a ballplayer's head coming off when he crashes into a fence. This scene is a tribute to a quote from San Diego Padres announcer Jerry Coleman: "Winfield goes back to the wall. He hits his head on the wall - and it rolls off! It's rolling all the way back to second base! This is a terrible thing for the Padres."
Trivia: There is a trailer to this movie with an additional gag. After Ludwig has demonstrated his image of an ideal assassin to Papshmir, he sits down with the revolver used in the demonstration which had turned out to be empty. In the trailer shot (in a closeup of Montalban) the gun unexpectantly goes off.
Trivia: Many elements of this movie, including Leslie Nielsen's character (named Frank) and the predecessor TV series Police Squad's title sequence and to some extent the title melody (also used in the Naked Gun movies) were adopted from the 1957-60 series "M Squad", starring Lee Marvin as Lt. Frank Ballinger.
Trivia: The scene where Drebbin is scolded by the mayor, and he comments about his direct action in a former case - shooting mad murderers (who turned out to be actors) - is a spoof on the first Dirty Harry movie; Clint Eastwood says something similar about a rapist, as I remember.
Trivia: The hypnosis plot is taken from both the Charles Bronson/Donald Pleasance thriller "Telefon" (in which the hypnosis is already implanted, and triggered by a special phrase, not an acoustic signal), as well as "The Manchurian Candidate" (in which Laurence Harvey is brainwashed and turned into an assassin, and then unable remember the event).
Trivia: The woman who shouts "hey look out" as Frank's car comes barrelling out of control toward him, is also in the second and third films. In the second film, she is a guest at the party. In the third film, she is at the beginning with a baby on the steps. Why is she in all three films? Probably because she's Naked Gun creator David Zucker's sister Susan Breslau.
Trivia: Robert K. Weiss, the film's producer, has a cameo as the hot dog vendor in the montage sequence.
Trivia: Director David Zucker has a cameo in the opening credits as a man fixing up a picture onto the wall of his house when the police squad car drives into the hallway. The director turns around and jumps into the room next door.
Chosen answer: "I'm Into Something Good." It's the second song listed in the music credits, and if you don't read all the credits you miss a good part of the gags in the movie.
"I'm Into Something Good" is played during the scenes where Frank is going out with Jane. The song the person is asking about is this song. Https://www.youtube.com/watch?v=wn-MlISDsNs.