After being confronted with the audio tape at the end, Nixon's head says, "Oooh, expletive deleted". This phrase became commonplace after the Watergate transcripts were publicly released in book form, and the phrase "expletive deleted" was used in place of the profanity uttered on the original tapes by H. R. Halderman and other Watergate insiders.
During the debate, Nixon sweats and appears uncomfortable during the debate. This is a reference to the first televised Presidential debates in 1960 between John F. Kennedy and Richard Nixon. At the time of the debate, Nixon was recovering from a knee injury two weeks earlier. He arrived at the debates in an ill-fitting shirt, and refused make-up that would have hidden his poor pallor and 5 o'clock shadow. Those who heard the debate on radio felt that Nixon had won the debate, while those who watched it on TV felt that JFK won.
When Fry asked why Nixon would stay in the "Watergate Complex", Leela explained that they give you a discount if you've been there before. Nixon took part in the "Watergate Scandal", which was a failed attempt by president Richard N. Nixon's staff to break into the Democratic headquarters at the Watergate office complex.
In the Hall of Presidents, you see Jesse "The Head" Ventura. As a wrestler, Jesse Ventura was known as "The Body". He was Governor of Minnesota from 1999 to 2003.
When Bender has a nightmare in binary, he later says, "Ones and zeroes everywhere! And I thought I saw a two." In almost the exact middle of the dream, you can see the two appear towards the bottom right of the screen.
In the Museum of Heads under "TV Stars", Katey Sagal who voices Leela is there.
The 'Rook Takes Pawnshop' is a reference to the game of chess.
The line "Dave's not here" said by the stoner to Amy is a reference to the famous stand-up routine from Cheech and Chong.