In addition to revealing Bart's reasons for being a troublemaker and underachiever, this episode is also notable for fueling suspicions of Milhouse's sexuality, after a school psychologist identifies the young Milhouse as having "flamboyantly homosexual tendencies." The episode is also notable for a rare glimpse at Snowball I.
The boy who eats worms was conceived by Al Jean in The Complete Ninth Season's commentary when he used to eat worms as a child and that he looks similar to him.
There is a portrait of Albert Einstein on the wall at school for smart children.
While telling Bart and Lisa about 1990, Homer says "the Tracey Ullman was entertaining America with ... crudely-drawn filler material," a reference to when The Simpsons started out as animated filler for The Tracy Ullman Show.
Bart's blackboard punishment "I no longer want my MTV" is a reference to the old MTV slogan "I Want My MTV" (and a jab at the channel's declining quality due to lack of music videos and an uptick in reality TV shows, like The Real World), which was also featured prominently in the Dire Straits song "Money for Nothing", which was also the first video to air in MTV Europe, in 1987.
The song "Those Were the Days" parodies the opening credits of the classic television show All in the Family. The show was also referenced with the narrator claiming that The Simpsons was filmed in a live action studio, and Homer referring to Bart as meathead.
Michigan J. Frog (or rather, a knock-off on him) briefly appears when announcing the new WB TV movie. In addition, his sing-song announcement, "We're proud to present on the WB, another bad show that no one will see!", is a jab towards the WB network's notoriety for being in the bottom six in ratings, and its shows being last chances that will not make it to other networks.
A flashback to 1990 shows Homer watching Twin Peaks as Dale Cooper remarks, "That's some damn fine coffee you got here in Twin Peaks... and damn good cherry pie." The Giant is then shown waltzing with a white horse, under a tree with a traffic light hanging from a branch. Homer says: "Brilliant! I have absolutely no idea what's going on."
When Lisa's saxophone gets run over, one of the people who runs over it is a man on a tricycle, who promptly falls over. This is a reference to a character played by Arte Johnson, an old man in a raincoat on a tricycle, which is a running gag from the NBC variety show Rowan and Martin's Laugh-In.
When little Bart skips along the grass, he bears a resemblance to Charlie Brown sketches.
In King Toot's music store, when Homer buys Lisa her first saxophone there is a guitar in the background that is similar to Eddie Van Halen's "Frankenstein" guitar.
When Marge, Homer and Lisa visit a preschool recommended by a school psychologist, a child can be seen in the left hand corner of the screen, that appears to be painting Rene Magritte's famous painting "The Son of Man."
Rod and Todd are still the same age in the flashback as they are in the present.
Despite this episode showing Bart as a bad student due to his bad first day of kindergarten, "Lisa the Simpson" reveals that Bart -- along with Homer, Grampa, and a bunch of other male Simpson relatives -- is genetically predisposed to become stupid as he grows older. On top of that, "Homer Loves Flanders" has Bart pointing out that being a loser is genetic (with Bart uttering "D'oh!" when he realizes that this affects him too).
5 years before 1997 would have been in 1992. It's possible Homer meant around 1990.
When Homer has to choose be between either an air conditioner or a Saxophone for Lisa. Lisa lacks any eyelashes.