This is the first episode of Futurama to feature time travel, a subject the show's creators did not want to broach too early/often due to the confusing direction that such stories can lead.
In a previous episode we discover that Bender is only 4 years old. Due to his head (but not his body) spending over 1,000 years buried underground, following this episode his age is around 1,060 years old, at least up until the events of Bender's Big Score.
In "Fry & the Slurm Factory", Fry was made infertile by Bender with the F-Ray. However in this episode he gets his Grandmother pregnant. In commentary it was stated that in the episode "Parasites Lost", the worms fix his testicles.
This is one of a number of appearances of Fry being synesthetic, e.g., "Hmph, what smells like blue?".
Roswell incident occurred in 1947, the same year that the microwave was invented (by Raytheon), or at least, publicly demonstrated
Bender saying that seatbelts cost more lives than they save is a reference to what Homer said in The Simpsons when he buys Snake's car.
While roaming around in 1947, Leela and the Professor wear clothing that they feel will help them 'blend in'; however, Hubert's zoot suit went out of fashion about five years previously, and Leela's poodle skirt ensemble wouldn't be in fashion until a bit later. (It's possible that by wearing it, Leela inadvertently began the poodle skirt's popularity. Choke on that, causality!)
The loss of Bender's head in the past and subsequent recovery in the present mirrors Star Trek: The Next Generation episode "Time's Arrow", in which Data's head is found first.