Starting with this episode Bea Arthur begins sporting a new hairdo. Arthur ditches her short perm and grows her hair out longer giving her a younger less matronly look. Arthur will maintain this look, with minor variations, for the remainder of the series.
Fidel is said to be in his 70's, but actor Henry Darrow was only 55 at the time and made up to look older.
The title is a parody of the song "Yes! We Have No Bananas" by Frank Silver and Irving Cohn from the 1922 Broadway revue "Make It Snappy" sung by Eddie Cantor.
When Dorothy refers to Rose's behind and says, "they could show How The West Was Won (1962) on yours". This is referring to how the film was shot in Cinerama and was projected on a very wide screen.
Although actor Henry Darrow was authentically Latin American, when Fidel says "My family once owned the largest tobacco plantation in all of Cuba," he mispronounces the name of the country in a way no native would, especially one with such a thick accent. The pronunciation in Spanish is "Cooba," not "Cyuba."