The store where Fry buys ham-flavored chewing gum has a sign that says, "Free bag of ice-9 with six-pack". Ice-9 is a fictional form of ice which is solid at room temperature, described by Kurt Vonnegut Jr. in his novel "Cat's Cradle".
The army hospital scene refers to the classic American TV series M*A*S*H (1972). The PA announcer is voiced by the same actor from the original series, and Dr. Zoidberg argues with a robot surgeon named iHawk, a parody of "Hawkeye" Pierce, the series' main character.
The trivia items below may give away important plot points.
When it aired originally, the last few minutes of the episode were pre-empted on the East Coast of the United States for a live news conference, held by Florida Secretary of State Katherine Harris, announcing the soon-to-be-controversial certification that named George W. Bush the winner in Florida of the 2000 presidential election. The interruption by Fox News occurred just after Bender screamed when he thought he said the word to blow up the planet, followed by a few seconds of black screen.
When Zapp talks to Leela (disguised as Lee Lemon) in the mess hall, he says he has read a new audio book about Greek warriors. This is referencing the fact that male Greek warriors would sometimes have sex with other male Greek warriors. Zapp is confused about his sexuality because of "Lee Lemon" (Leela).