The Hippie Universe is Universe 420. The number 420 is also a slang term associated with smoking marijuana.
Mom flipped a coin whether she should keep Igner or the afterbirth. Thus, Igner might not exist in Universe 1.
The title is a pun on the term "paradox" and "box."
When this episode was aired once on Comedy Central, the parts of Hubert Farnsworth screaming for help from Buddha, Zeus, God and Satan are removed from the scene, focused only on Fry and Leela instead of the professor's screams for help.