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.
Leela says "For heavens gate" because they are in traffic, but normally it is "For heavens sake".
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 the film of the 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", the 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. Among the stories 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 among she reads some classical childrens book Snow White Dwarf and the Seven Red Dwarfs which is a refernce to the popular story Snow White and the Seven Dwarfs. And also The Fountain of Aging which is a refence 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.
The theatre with the movie Fiddler Way Over the Roof is referenced by a later episode, "That Darn Katz!", where Dr. John A. Zoidberg says they can do a Broadway play. And Nibbler says "we can call it Nibbler On The Roof."