The episode name is a reference to the fungal skin infection athlete's foot.
In the Rick and Morty couch gag, in the dimension Morty is in, there is a ship flying over Morty's head, which is actually the Planet Express Ship from Futurama and a soda machine that says Slurm on it (also Futurama). Kang and Kodos can be seen in the same scene.
In this episode, Lisa uses Superintendent Chalmers catchphrase (Skinneeeerr!!). Chalmers also uses it while referring to behavioral psychologist B.F. Skinner, who incidentally was also the namesake of the character.
Before the power goes out, one of the kids is watching a clip from the episode "The Bob Next Door", where Sideshow Bob, disguised as Walt Warren, had Walt's face peeled off by the waitress.
The Math joke is I ate some pie.
In the Rick and Morty couch gag, the Simpsons turn into goo instead of having blood everywhere.
This episode, along with Lisa the Simpson shows that Bart is better than Lisa in solving mathematics and geometric puzzles.
Objects that Rick stole from the Simpsons house in the Couch Gag:
In the Anti-Gutenberg 3000 Machine that appears in this episode, the temperature display reads 451°F. This is a reference to Ray Bradbury's 1953 novel Fahrenheit 451 which is about a dystopian future where all books are burned, along with the houses they are kept in.