"Mahatma Kane Jeeves" (the pseudonym used by W.C. Fields as screenwriter) is a play on words from stage plays of the era. "My hat, my cane, Jeeves!" And in fact, at the end of the film his butler does hand him his hat and his cane.
Near the beginning of the movie, Egbert Sousé is whistling "Listen to the Mockingbird" as he & Joe the Bartender enter the bar. Joe is played by Shemp Howard of The Three Stooges fame, and "Listen to the Mockingbird" was the Stooges' theme music in the mid- to late 1930s (though Shemp wasn't part of the team during that time).
Universal's censors initially objected to W.C. Fields' script and demanded many changes. Director Edward F. Cline suggested that Fields should go ahead and film it their way, ignoring the censors' changes, and that the front office wouldn't notice the difference. They didn't.
Lompoc is properly pronounced "Lompoke". It was also founded as a Temperance town, probably another reason Fields picked it as his hometown in this film, and the towns people of the day disliked Fields for these two reasons.
In a 1970s interview with Richard Schickel, Orson Welles claimed that W.C. Fields called himself "Mahatma Kane Jeeves" in his screenwriting credit as a tribute to Welles. Welles did amateur magic shows as "The Great Mahatma," directed and starred in Citizen Kane (1941) and "Jeeves" came from the butler character in P.G. Wodehouse's novels, which both Welles and Fields admired.
The bar Shemp Howard's character runs was originally called "The Black Pussy Cafe," but the Production Code Administration said the name couldn't be used. W.C. Fields protested because he'd got the name from his friend, British comedian Leon Errol, who owned a real bar in L.A. called the Black Pussy Cafe. Fields said that if the California Alcoholic Beverages Control Board didn't object to that as the name of a real bar, the Production Code Administration shouldn't mind it as the name of a fictional one. The Code authority was unmoved, so the signs on the bar in the film call it "Black Pussy Cat Cafe"--but both Fields and another actor refer to it as the "Black Pussy Cafe" in the dialogue.
The scene in which a motorcycle cop drives through a trench full of ditch-diggers and knocks them out of the trench was developed by Buster Keaton and director Edward F. Cline for Keaton's film Sherlock Jr. (1924), which Keaton and Cline co-directed. Cline recycled the gag for this film.