The episode title is a pun on the 1997 American crime drama film Donnie Brasco.
The plot of the episode parodies that of the film, with Homer taking the role of Joseph D. Pistone, who uses the undercover name "Donnie Brasco" to infiltrate the American Mafia, and Fat Tony taking the role of mobster Lefty Ruggiero, who befriends Donnie while remaining suspicious.
Marge wants her children to stay quiet about her being hungover until the Fiesta Bowl, an annual American college football bowl game usually taking place at the beginning of January.
The Blue Angels demonstration squadron fly over Samoa on New Year's Eve.
Homer and Moe interrupt a play of Wicked. Characters of the musical and several references to The Wizard of Oz are seen.
Glinda says to Moe, "You've always had the power to get back to the bar", a reference to her iconic phrase in the 1939 film, "You've always had the power to get back to Kansas", directed at Dorothy Gale.
Moe and one of the flying monkeys parody the "Mirror Scene" from the 1933 film Duck Soup, featuring the Marx Brothers.
The sign seen outside, "Out of control since 2001", makes an allusion to the expansion of FBI and US government surveillance and power during the aftermath of the September 11 attacks.
The board of Fat Tony resembles the mosaic board in FlashForward.
When Homer was struggling to pronounce the word "consigliere", he states that he is Fat Tony's Robert Duvall, the actor who played Tom Hagen, the consigliere (advisor) for the Corleone family in The Godfather.
Homer is given the initiation ritual to become a member of the Mafia. The ceremony involves Homer's finger being pricked with a knife by Fat Tony and spilling a few drops of blood on a picture of Francis of Assisi.
Fit Tony says, "That's why I keep my friends close". When Homer asks him "and your enemies closer?", he is referring to the phrase from The Godfather Part II, "Keep your friends close, but your enemies closer".
One of the horses at the gambling event is named "Mrs. Ed", a pun on Mister Ed, the talking horse of the series of the same name.
The line Homer says, "Now I'm just an average snook like everyone else", and the episode's closing sequence are a reference to the film Goodfellas.
The song "My Way" by Sid Vicious is heard, a song that also plays during the ending of Goodfellas.
Nicholas Pileggi, who co-wrote the screenplay for Goodfellas, is mentioned along with his wife, Nora Ephron.
There have been other canon episodes where something happens to a major character, but the consequences are dealt with by the end of the episode and everything goes back to normal:
"I, (Annoyed Grunt)-bot" -- Snowball II dies, followed in quick succession by two more Simpson family cats (Snowball III and Coltrane). Lisa then gets a cat that looks exactly like Snowball II, names it Snowball II (even though it is technically Snowball V), and decides to pretend the whole thing never happened.
People on the FBI's chart of Fat Tony's associates include:
