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"
In order to show the crew his new commercial, the Professor uses a VCR with a "VCRPLUS++" logo. As programming VCRs to record future programs proved challenging to many due to the difficult on screen menu, VCR Plus was a system of individual numbers assigned to every program that were published in TV listings that could be used to schedule recordings. The introduction of TiVo the same year the series premiered spelled the eventual end of VCRs and the need for VCR Plus.