During the first flashback, Teeth and Floyd meet at Jerry's Tunes music store. A reference to Floyd's original performer Jerry Nelson. One of the signs notes that the shop was established in 1934, Jerry Nelson's year of birth.
This episode establishes that Dr. Teeth is not only a qualified dentist, but also grew up in New Orleans. The character was partly inspired by real life New Orleans musician, Dr. John.
Nora has a tattoo that says "One Love," a reference to the Bob Marley song. There is, coincidentally, another song of that title written by frequent Muppet collaborator Paul Williams (who also wrote "Can You Picture That?").
After his graduation, Dr. Teeth calls Floyd "Sarge," a reference to the Beatles album Sgt. Pepper's Lonely Hearts Club Band.