When Ethelrida enters the principal's office, she says: "What's the rumpus?" This is a oft used line in the Coen brother's film Miller's Crossing.
The song used in the opening scene is an instrumental jazz version of the song Moanin' by Bobby Timmons, another version of this song by Lambert Hendricks & Ross was used in Fargo (2014) season three The Law of Vacant Places (2017).
Towards the beginning of the episode, there's a truck with the name Treehorn on the side. This could be a reference to The Big Lebowski, in which there is a character named Jackie Treehorn. The Coen Brothers directed that film as well as the same-named film on which this show is based.
In Gaetano's barroom soliloquy he says "in Italy we pay you to sweep, you sweep. We pay you to make a coffee, you make a coffee like Michelangelo." This echos an MLK Jr. speech where he said "If a man is called to be a street sweeper, he should sweep streets even as Michelangelo painted."
When Ethelrida enters the principal's office, where the marshall is waiting to question her, the old lady says to her " I knew you were trouble the moment I laid eyes on you". This is a direct quote from "Wall Street" (1987). Bud Fox's office manager says the same thing to him as the marshall is in his office waiting to arrest him.