The Femputer being just a false front operated by an ostensibly omnipotent while hidden operator is a reference to the title character in the film The Wizard of Oz, down to the hand-operated controls and outdated microphone.
Several of the electronics on Amazonia carry the brand name Sonya. As mentioned in the audio commentary for this episode, the name is a feminized version of electronics company Sony.
When searching the jungle, Fry and Bender find a large empty can of TaB cola.
Zapp Brannigan's spoken-word rendition of "Lola" by The Kinks is reminiscent of similar performances by William Shatner, whom Zapp is a parody of.
The spaceship-restaurant is reminiscent of the bistro-starship from Douglas Adams's The Hitchhiker's Guide to the Galaxy.
The impact tremors of the approaching Amazonian women causing ripples in a cup of water and a puddle is a reference to the film Jurassic Park, in which the approaching Tyrannosaurus causes the same phenomenon.
The punishment of "death by snu-snu" is similar to the well-known joke involving two male explorers who find a jungle tribe, and are subsequently condemned, being given a choice of death or "oonga-boonga". One chooses Oonga-boonga and is raped and sodomized by all of the male tribe members. The second declares that to spare his dignity, he would rather choose death; the tribe then declares "Death... by Oonga-boonga!"
The comments made about the basketball on Amazonia are a reference to the critiques of the WNBA, and women's basketball in general.
The company named J. Crab that manufactures shells for Decapodians is a parody of J. Crew.
Leela flips through a real estate circular called "Westside Cave Rentals", a play on the popular California real estate website Westside Rentals.