When the Professor hits the "Marconi" and says it doesn't work it is a reference to Guglielmo Marconi who is seen as the inventor of Radio.
The episode parodies the supposed prophecy according to the Mayans where the world will end in the year 2012 and also the movie 2012.
The scene where Fry gives Leela a picture of them at the prom together and said "Remember when Bender dumped the pig's blood on me?" is quite possibly a reference to the novel by Stephen King (and the film adaption) named Carrie, where Carrie goes crazy during her Senior Prom after Chris dumped the pig's blood on her and ends up killing everyone with her telekinesis.
The episode's title is taken from the novel A Farewell to Arms, as well as the ending scene where Fry and Leela's arms are torn off and lost in space.
The situation in which a solar flare will strike and destroy Earth is reminiscent in the film Knowing.
In the aftermath of the departure of the chosen few to mars, in one scene, Bender, who has decided to stay on earth for looting, is shown driving a Rolls Royce Phantom V into a jewelry store.
The scenes where Mars passes above New New York is similar to the scenes of the film Independence Day where a giant alien spaceship passes above New York City.
There is a dark subtext to this episode that implicates the native Martians as trying to trick earthlings into traveling to Mars in that they left a space ship on the safe planet that would be the only way to travel to the doomed planet.