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The episode is a parody of the TV show The Untouchables, with Rex Banner based on Prohibition agent Eliot Ness. Homer even references the ending of the series when predicting correctly that prohibition won't last when he said "It didn't work in the movies."
Homer's nickname; "The Beer Baron" is a reference to New York mobster; Dutch Schultz who was known as "The Beer Baron of the Bronx" as Schultz was involved in the bootleg alcohol trade in the New York Bronx area during Prohibition and had later attempted to move in on the Numbers Racket before he was shot along with members of his gang by Murder Incorporated hitmen; Charles "The Bug" Workman and Emanuel "Mendy" Weiss at the Palace Chop House in Newark, New Jersey on the night of the 23rd October 1935, Schultz later died of his wounds in hospital during the early hours of the 24th October 1935.
Homer's toast at the end, "To alcohol, the cause of and solution to all of life's problems," is a very well known line, and has been referenced by many.
When Nelson Muntz makes fun of Bart at the beginning, one of the shamrocks on his bowtie briefly disappears.
Lenny is shown to be both at Moe's Tavern and at the parade (pointing out the free beer at the latter event).
The bottle of Duff Beer that Apu holds has a blue label instead of the usual red one, plus the text is much thinner than it usually is.
In the crowd scene, Ms. Hoover is missing her glasses.
The Prohibition is limited to Springfield. Yet, it never seems to occur to anyone that they could easily go to Shelbyville if they wanted to drink.
While Rex is investigating Moe's "pet shop", the patrons at the bar raise their hidden beer glasses to toast the "best pet shop in town" while Rex has his back turned. However, Eddie and Lou were clearly facing the patrons and were looking at their beer glasses in the frame they raised them. Of course, Eddie and Lou more than likely weren't on board with the whole prohibition law to begin with.
When Moe is putting the bar scenery back up, one of the bottles is not colored in for a frame.
When the crowd cheers after Rex Banner announces to have succeeded, some of the people's hair in the background flashes yellow for a few frames.