The Bartman segment contains several plot references to the Tim Burton Batman movie. Bartman sees his parents shot by an unknown crook in a dark alleyway, similar to how Jack Napier (the Joker) kills Bruce Wayne's parents. Bartman does not find out that the Serpent was his parents' assassin until later, just as Batman doesn't realize the Joker was the man who shot his parents. Additionally, the final scene takes place in a museum, a setting also used in the Tim Burton Batman film.
The Rich Texan mentions that he's from Connecticut. This is most likely a reference to George W. Bush, who lived most of his life in Texas but was born in Connecticut.
In the Count of Monte Cristo, it is said that they live in the 16th Arrondissement, which is problematic for two reasons. First, the arrondisements are not numbered in themselves (Districts, the next-higher administrative unit, are numbered). Second, during the time frame of the story, the Department of Paris only had 12 arrodissements (hence it would not make sense for theirs to be the 16th of the district either).
Milhouse's Power Glove is a visual reference to the Nintendo Power Glove from the 80s.
The scene where Bartman hits Moleman with a hammer is a reference to the game Whack A Mole.
The Bartman in this episode is different than the one in Three Men and a Comic Book. In that episode Bartman was simply Bart wearing a purple mask around the top of his head. This Bartman is Bart in a complete Batman outfit.
In between stories (the only time in the episode where what happens could be considered canon) Homer says he shot Mr. Burns and pinned it on Maggie. A reference to the season 6 and 7 two parter episode "Who Shot Mr. Burns"?
The end credits list those who died in the star wars films. However, Sy Snootles is listed, even though she survived Jabba's sail barge explosion. Also in the end credits, Qui-Gon Jinn should have been featured on the list, being killed in The Phantom Menace by Darth Maul. In an episode of Star Wars spin off The Clone Wars, Darth Maul was revealed to have survived, so he no longer counts on the list.
This is the second episode where a Springfield Elementary Student gets the mumps. The first being Bart's Dog Gets an F.