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operator is a reference to the title character in the film The Wizard of Oz, down to the hand-operated controls and outdated microphone.
The Femputer also has a connection with a Twilight Zone episode, "The Old Man In The Cave".
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. TaB is a soft drink originally marketed toward women, and was created in 1963 to compete with the (then) only sugarless soda on the market, Diet Rite 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.