Curly "Gallstone"'s red book of women's addresses and phone numbers has the rather overt sexual references "Ruby Clutch", "oh, oh oh! G" (bra size) and the unread "Tessie oomph 2 69" which were ignored by the censors. This was a key dig at the attempt to censor The Great Dictator (1940) then in production by Charles Chaplin (Curly was also noted in his personal life for being a womanizer).
A billiards 8-ball was used as a fortune telling device in the scene with the female spy, Mattie Herring. This predates by ten years the popular toy fortune telling device, "The Magic Eight Ball", first marketed by Alabe Crafts Company in 1950.
The Three Stooges, who were all Ashkenazi Jews, occasionally worked a word or phrase of Yiddish into their dialogue. In particular here, they make several overt Jewish and Yiddish cultural references: The exclamation "Beblach!" used several times in the film is a Yiddish word meaning "beans". "Shalom Aleichem!", literally "Peace unto you" is a standard greeting in Yiddish meaning "hello, pleased to meet you". "Moe: We'll start a 'Blintzkrieg' (Blitzkrieg). Curly: I just love blintzes especially with sour krieg." This is a reference to the Ashkenazi Jewish dish blintzes with sour cream. In Moe's imitation of a Hitler speech, he says "in pupik gehabt haben" (the semi-obscene "I've had it in the bellybutton" in Yiddish). These references to the Nazi leadership and Hitler speaking Yiddish were particularly ironic inside jokes for the Yiddish-speaking Jewish audience.