Fry's line "shields at maximum Yarnell" is a reference to the popular mime duo (and real life husband and wife) Robert Shields and Lorene Yarnell Jansson. One of their most famous routines involved them playing married robots, which relates to the plot of this episode.
When Fry, Bender, and Leela are standing in the shower, formulating their plan, and the ships computer says "I wish I learned to read lips" is another nod to 2001: A Space Odyssey (1968) - specifically the scene where Frank Poole and Dave Bowman are in the work pod working out how to handle HAL's aberrant behavior.
Bender (as an electron) races through a diode against the direction marked on it and is unable to go back. This is accurate : electrons flow inverse to the "direction of electricity", which is an arbitrary convention over a complex matter.
At the Romanticorp factory, a scientific experiment is shown where a woman responds to pick-up lines given by dummy would-be boyfriends. The dummies are not realistic mannequins, but are made of bare chicken wire with large googly eyes stuck on. This is a reference to the mother-child-bonding animal experiments of Harry Harlow in the 1950s, where baby macaque monkeys were nursed by bare-wire dummies holding bottles.
Quasars were first detected in the 1950's as being extremely powerful extragalactic radio sources and in the 70's were discovered to be among the most energetic producers of X-Rays in the universe, but their nature was unknown for some time. Early theories were that quasars were the endpoint of a wormhole, or possibly a galaxy made of antimatter. However after the discovery of the first black holes, especially the supermassive black holes at the center of most galaxies further study revealed that quasars are actually some of the largest supermassive black holes in the universe, their gravitational force is so great that the matter in the accretion disc of the black hole is superheated and releases massive amounts of electromagnetic radiation, which is the source of the radio and X-Ray emissions detected from quasars. A few of the largest quasars are even able to repel matter away from them, how this is done or even possible is not known, but the matter emitted from them is called a astrophysical jet. Astrophysical jets consist of superheated ionized matter, usually thousands of light years long, being ejected from the center of extremely large supermassive black holes at relativistic speed, meaning the matter is traveling near the speed of light and is affected by special relativity, the fastest jet found so far has matter traveling at 80% the speed of light.