The movie was titled "The Cheap Detective", according to screenwriter Neil Simon, "because the detective in those old films never got paid! Who paid Humphrey Bogart for finding all those crooks in The Maltese Falcon (1941)? He arrested Mary Astor and sent her and everyone else to jail. Who paid him? The character is always involved in danger not for the bucks but because it's his lifestyle."
The farewell scene between Lou Peckinpaugh (Peter Falk) and Marlene DuChard (Louise Fletcher) was shot on the same soundstage that was used for the Humphrey Bogart and Ingrid Bergman farewell in Casablanca (1942).
This movie's character spoofs are as follows:
Eileen Brennan's Betty DeBoop is a combination character spoof of Lauren Bacall's Marie "Slim" Browning, in To Have and Have Not (1944) and Marlene Dietrich in many films;
Madeline Kahn's Mrs. Montenegro et al is a spoof of Mary Astor's Brigid O'Shaughnessy, in The Maltese Falcon (1941);
John Houseman's Jasper Blubber is a spoof of Sydney Greenstreet's Kasper Gutman (aka "The Fat Man"), in The Maltese Falcon (1941);
Dom DeLuise's Pepe Damascus is a spoof of Peter Lorre's Joel Cairo, in The Maltese Falcon (1941);
Fernando Lamas's Paul DuChard is a spoof of Paul Henreid's Victor Laszlo, in Casablanca (1942);
Paul Williams's Boy is a spoof of Elisha Cook Jr.'s Wilmer Cook, in The Maltese Falcon (1941);
Scatman Crothers's pianist Tinker is a spoof of Dooley Wilson's piano player Sam, in Casablanca (1942);
Ann-Margret's Jezebel Dezire is a spoof of Claire Trevor's Helen Grayle, in Murder, My Sweet (1944), a Philip Marlowe film starring Dick Powell who also voiced Richard Diamond on the radio;
Louise Fletcher's Marlene DuChard is a spoof of Ingrid Bergman's Ilsa Lund, in Casablanca (1942);
Peter Falk's Lou Peckinpaugh is a spoof of two Humphrey Bogart characters, Sam Spade in The Maltese Falcon (1941) and Rick Blaine in Casablanca (1942) but is also an extension of his Sam Diamond character from Murder by Death (1976) as well as his Columbo (1971) character, being the coat gag throughout the film.
The detective partners are named Peckinpaugh and Merkle. Roger Peckinpaugh and Fred Merkle were two well-known baseball players in the early twentieth century.The piano player is named Tinker. Joe Tinker was a famous shortstop for the Cubs. Other characters include Sergeant Rizzuto, Sergeant Crosseti, and Lieutenant DiMaggio, all famous Yankees.
Madeline Kahn's character used sixteen names: Denise Manderley, Wanda Coleman, Gilda Dabney, Chloe LaMarr, Alma Chalmers, Alma Palmers, Vivian Purcell, Carmen Montenegro, Diane Glucksman, Mrs. Danvers, Natasha Ublenskaya, Sophie DeVega, Mary Jones, Lady Edwina Morgan St. Paul, Norma Shearer, and Barbara Stanwyck. The last two were famous actresses' names from the 1920s and 1930s, suggesting that her character was running out of ideas. The name used most is Mrs. Montenegro.
Phil Silvers: As Hoppy, a cab driver. Despite getting billing on the opening credits, the comedy legend only has one line in one brief shot.