Leela's backpack has a "Curious Pussycat" logo on it.
Zoidberg's alien species has multiple larval stages, one of which is where he and his siblings are all connected in a big lump and another of which was a lamprey. Supposedly once they reach adulthood they retain their current form, as a later episode suggests.
Amy was overweight as a kid and also wore glasses at one point.
It's revealed that the Tooth Fairy is real, and is actually a man rather than a woman. The Tooth Fairy is also the head of the FBI.
When Bender was a kid, he wanted to be a steam shovel.
Some reasons why Professor Farnsworth likes being old:
He doesn't have to talk to his parents.
No one asks him to help move their stuff.
He doesn't have to understand current TV sitcoms.
Reference[]
The title for "Teenage Mutant Leela's Hurdles" comes from the popular television show Teenage Mutant Ninja Turtles.
Leela says "For heavens gate" because they are in traffic, but normally it is "For heavens sake". Heaven's Gate may refer to the disastrously unsuccessful 1980 film of that name, or to a religious cult infamous for their 1997 mass suicide when 39 members died because they thought they would be transported to a spaceship concealed in a comet's tail.
Pazuzu is the name of a wind demon in Babylonian mythology and the demon featured in The Exorcist. The character resembles the statue of Pazuzu from both the film and novel.
Professor Farnsworth's tar-eating bacteria resemble the popular video game character Pac-Man.
Leela saying "Look how high the asteroid belt is pulled up on that planet" is supposed to be a reference to the stereotype that old people pull their pants (which may have belts on them) up too high.
Young Zoidberg looks a little like "Blinky", a mutated fish from The Simpsons.
Leela reads in the book A Child's Garden of Space Stories which can be a reference to the children book A Child's Garden of Verses. The book's cover features a Gorn, from the classic Star Trek episode "Arena". Among the story titles Leela reads to the young Planet Express crew is "Charlotte's Tholian Web", a reference to the Tholians from Star Trek, as well as the book Charlotte's Web by E.B. White. Also, Snow White Dwarf and the Seven Red Dwarfs which is a reference to the popular story "Snow White and the Seven Dwarfs", as well as a reference to nomenclature of two types of stars. Along with The Fountain of Aging, which is a reference to the legendary myth about the Fountain of Youth.
Pazuzu's relocation to Paris, specifically the Eiffel Tower, is a possible reference to Jeques Tardi's 1976 Graphic Novel The Demon of the Eiffel Tower, which featured the babylonian demon Pazuzu after which it was named. In the episode, Pazuzu and his son are seen on the Notre Dame cathedral; that structure is actually decorated with numerous carvings of gargoyles.
The theatre with the movie Fiddler Way Over the Roof is referenced by a later episode, "Overclockwise", where Dr. John A. Zoidberg says they can do a Broadway play. Also, Nibbler says: "We can call it Nibbler On The Roof!"
