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.

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.

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.

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).