The title of the episode is a reference to All The President's Men, a 1974 book and 1976 film.
When Fry arrives at the Head Museum to start his shift as the night security guard, Dr. Cahill refers to him as "Lars." Lars' was Fry's doomed time travel duplicate who worked at the Head Museum during the events of Bender's Big Score, and sacrificed himself to save Leela and stop the scammer alien Nudar from utilizing the time code again.
When the Planet Express Crew arrive in "West Britannia", a double decker bus is shown stopping across the street from the Planet Express building, right next to a Police Box. A man in a long, colorful scarf gets out of the bus and steps into the Police Box. This is a reference to the British TV show, Doctor Who. The man is a clear reference to the Fourth Doctor, played by Tom Baker. The Doctor's TARDIS looks like a police box.
When the Planet Express crew is shown partying in the Head Museum, one of the heads shown in the hall of presidents is Amelia Pond. Amelia Pond is the actual name of Amy Pond, the Eleventh Doctor's first companion in the British science fiction series, Doctor Who.
Professor Farnsworth tells Fry "you really screwed the Granny this time," making a euphemism out of their time travel escapade in which Fry impregnated his own grandmother.
Hermes is wearing a Manhattan United T-shirt, which is a reference to the football team Manchester United.
The Cartoon That Appears In The Documentary America The Dutiful Is A Reference To Monty Python's Flying Circus.