The car that Polly drives at the end is a 1958 Fiat 600, a most unusual car to be found in a small American town at the time - so: likely nod / recognition to original playwrite Anna Bonacci's Italian play, 'L'Ora della Fantasia' this film was based on.
Production began with Peter Sellers in the role of Orville. Sellers suffered a heart attack several weeks into production, and filming was re-started with Ray Walston in the role (after Tony Randall, Bob Hope, Jack Lemmon,Danny Kaye and Tom Ewell were all considered).
The role of Polly the Pistol was originally written for Marilyn Monroe. However, her death in August of 1962 delayed the project. Jayne Mansfield was then considered, but had to withdraw due to pregnancy.
According to a Peter Sellers interview in 1962, the original idea Billy Wilder had about casting was to co-star him with Frank Sinatra (in the role eventually played by Dean Martin), Marilyn Monroe (as Polly) and Shirley MacLaine (as Zelda). None of them ended up in the finished picture, of course.
As Dino is leaving Las Vegas in the beginning of the film, he encounters a police roadblock. He stops his car and asks the officers, "What's the matter? That Sinatra kid missing again?" This was an allusion to the 1963 kidnapping of his fellow Rat Pack member's son, Frank Sinatra Jr..