This is yet another episode in which time-paradoxes that should destroy the universe, don't. Other examples would be Fry impregnating his own grandmother, and Professor Farnsworth clubbing his own descendant over the head.
The movie "Soylent Green" is referenced when Nixon begins making "Soylent Majority."
A candidate says "ENVIORMITE!", a reference to the famous "DYNOMITE!" quote, said by "J.J." Evans on the TV show, Good Times.