When Bart is at the North Pole, Schroeder of the Peanuts can be seen playing his piano.
At the end of the episode, as a tribute to the Sesame Street, stated by Simon Singh's book "The Simpsons and their Mathematical Secrets", it ends with the traditional sponsorship announcement. However, the announcement says "Tonight's Simpsons episode was brought to you by the symbol umlaut, and the number e; not the letter e, but the number whose exponential function is the derivative of itself."
When the Security snowmen are melting, Lisa briefly disappears. She reappears later when Bart eats one of the guard's "nose".
Televisions already existed in 1944, but they were very rustic and expensive.
Martha Stewart managed to get pine tree branches from Marge's window, but the only thing close to the window was her improvised ladder with a fence.