It's learned that the human population of Earth is at least 40 billion.
As they are climbing Leela's "hair", Fry and Bender cross paths with Adam West and Burt Ward, who played Batman and Robin, respectively. The entire scene is a parody of a similar recurring campy scene featured throughout Batman (1966): Batman and Robin would be scaling a wall (literally "walking" up the wall) and a window would open and some random celebrity would have a brief cameo.
Mom's genetic engineering lab, Momsanto, is a clear reference to the multinational corporation Monsanto. The company was one of the first to genetically modify crops and seeds, a controversial practice alluded to by both Mom and Leela.
It's learned that Leela, being a mutant, occasionally lays an egg.
The crew goes to a western bar called TEX 1138's, which is a spoof of George Lucas's first film THX 1138 (1971). In fact one of the bar workers has a shaved head and ear tags like the characters in the movie.