Wealthy New York City playboy Arthur Bach (Dudley Moore) is perpetually drunk and completely rudderless. Dutifully supported by his sharp-tongued and quick-witted butler, Hobson (John Gielgud), Arthur reluctantly prepares to enter into an arranged marriage with heiress Susan Johnson (Jill Eikenberry). When he meets Linda Marolla (Liza Minnelli), a waitress from Queens, he falls head over heels in love, but if he backs out of his engagement with Susan, he may lose his fortune.
Six criminals with pseudonyms, and each strangers to one another, are hired to carry out a robbery. The heist is ambushed by police and the gang is forced to shoot their way out. At their warehouse rendezvous, the survivors, realizing that they were set up, try to find the traitor in their midst.
Frank Drebin (Leslie Nielsen), a rather clueless police detective, tries to foil a plot to turn innocent people into assassins through mind control. After his partner, Norberg (O.J. Simpson), is shot, Frank sets out to find the culprit, leading him to business tycoon Vincent Ludwig (Ricardo Montalban). However, Frank has no evidence until he meets Jane Spencer (Priscilla Presley), Ludwig’s assistant. She knows nothing about Ludwig’s devious plans, but falls for Frank and agrees to help him.