The main part of the film was shot during the summer months of 1962 because many cast members were on hiatus from television series which they were working on.
The role of Ray (one of the gas station attendants) was intended for Jackie Mason. Mason withdrew due to his nightclub commitments and Arnold Stang replaced him at late notice.
The roles of Melville and Monica Crump were originally larger roles and written for Mickey Rooney and Judy Garland in mind. However, when production on Garland's TV variety show ran into trouble, she had to turn down the part. Rooney was eventually given the supporting role of Ding "Dingy" Bell. Edie Adams, who was originally cast in the role of Emeline, was given the role of Monica. Ernie Kovacs was then cast as Melville but was tragically killed in a car crash before shooting began and was replaced by Sid Caesar.
The scene where Melville accidentally knocks the blowtorch into the stairs with the sledge hammer took 86 takes to get it just right.
Top billed Spencer Tracy worked on the film for a total of nine days. Aware of his poor health stemming from type 2 diabetes and emphysema, director Stanley Kramer only allowed him to work for three to four hours a day and did not let him appear in any of the hot and arid desert exterior scenes. A stunt double was used for Tracy in a few action scenes, one of which includes him running up the building stairs where you don't see his face.
When the cast first assembled for a meeting with the director, they were shown the stunts and second unit footage that had already been shot. One of the performers was so impressed they asked "Why do you need us?"
Jack Benny:
the car driver who stops to offer help to Mrs. Marcus.
Jerry Lewis:
the car driver who deliberately drives over Culpepper's hat.
The Three Stooges:
airport firemen, with the shortest cameo in the movie: five seconds.