The opening frame of part 3 says, "0100100001101001" which is binary for "Hi" in ascii.
According to her phone bill, Fry called Dial-A-Joke 8,128 times while he lived with Colleen.
The title is a combination of the Roger Corman film The Beast with a Million Eyes (1955) and the phrase "the beast with two backs," a term referring to the act of sexual intercourse between two people (coined by William Shakespeare).
Leela's fake tentacle hose has a label that reads: "Apex Garden Hose: The Gopher Drowner."