At the amusement park they get, not spun sugar cotton candy, but spun orlon candy. Orlon was the first acrylic fiber for lightweight textiles and was used instead of cotton until polyester arrived.
Although the lunar lander shouldn't be in one complete part, the entire thing (and the flag) is still there. This is explained by a plaque inside the lander that says: "Lander returned to this site by the Historical Sticklers Society".
The scene when Bender hits a bottle of liquor in the eye to a man with a moon-like face, is a reference to A Trip to the Moon (1902).
Originally, this wasn't intended as the second episode. Or at least, not its plot, that was actually intended for the plot of My Three Suns (1999), but David X. Cohen and Matt Groening wanted to start off more down to Earth, so that episode was moved to slot 7 and this became episode number two.
A restaurant sign in Alien Language 1(AL1) can be seen in the background when bender is explaining how magnets affect him. It translates to "Tasty Human Burgers"