In the background of the meeting between the two Hormone Monsters, a billboard for "Oh, Hello" on Broadway can be seen outside, although it is partially obscured by the window frames. "Oh, Hello" stars Nick Kroll and John Mulaney, who also star in Big Mouth.
After commenting on the Hamilton posters in Leah's room, Missy says it's definitely "the room where it happens", referencing a song from the musical.
The cutaway scenes in the diner are a reference to the sitcom Seinfeld (1989-1998). Tom's Restaurant in the cutaway is also the name of the diner is Seinfeld, so this reference is direct. In the cutaway Nick is portraying Jerry (Jerry Seinfeld), Andrew is George (Jason Alexander), Jessi is Elaine (Julia Louis-Dreyfus) and Jay is Kramer (Michael Richards).