In the episode "Helter Shelter", Homer is upset that 1895 is too late to save Lincoln and too early to save Kennedy, and in this episode he fantasizes about doing both tasks.
Bar mitzvah ceremonies are largely arbitrary, and not having one has no bearing on a Jewish male's standing as a "real" Jew.
When Krusty is sitting in front of his TV, in the background there is an upside-down German flag on the wall.
When Krusty proclaims that he would be a bad Jew if he continued to perform shows on the Sabbath the first replacement suggested for Saturdays is comedian Jon Stewart, whom Krusty rejects thinking that he will be upstaged. Stewart is Jewish himself, although he is not religious, thus making Krusty technically correct.
Lisa has a Jewish imaginary friend named Rachel Cohen who goes to Brandeis University.
It is implied in this episode that Krusty has a cocaine problem: He is shown putting a finger on his nostril and inhaling, to then claim to Bart and Lisa, who are right in front of him, "You know, sniffing flowers. Such expensive flowers filled with remorse."
The subplot involving Santa's Little Helper being neutered after an incident with his owner's neighbor's pet dog got her pregnant resembles a similar plotline in the sitcom Frasier (specifically, it's the episode "The Unkindest Cut of All"). In fact, both neighbors in that episode even say to the family that owns the dog "Well, I'm glad you like them, because they're your problem now!" Coincidentally Kelsey Grammar and David Hyde-Price, who play Sideshow Bob and his brother Cecil on The Simpsons played Frasier and Niles Crane on Frasier.
Los Angeles Dodgers pitcher Sandy Koufax's refusal to pitch Game 1 of the 1965 World Series because it fell on Yom Kippur is mentioned when Krusty sees his star on the Jewish Walk of Fame and reacts with disgust.
The dog neutering clinic which Santa's Little Helper is taken to is called Nuts Landing, a reference to Knots Landing.
Dr. Hibbert's dog, Rosa Barks, is a reference to Rosa Parks, a Civil Rights Activist.
FOX makes fun from itself again: its main headquarters is shown like an old caravan in the middle of desert.
Homer referencing to Argentina is maybe related to the latter country recently (by tat time) recovering from a financial crisis it suffered in years 2001-2002.
There are three bathrooms in the Simpson house, so there was no reason for Homer, Marge, Bart, and Lisa to all have to wait in line.
In the Itchy & Scratchy Show cartoon "A Briss Before Dying" Itchy pulls Scratchy's eyes out and throws them out of the window, but the windows is clearly seen to be closed.