The animation of the Planet Express Ship entering the Nimbus' cargo hold may be a visual reference to the film Moonraker, although a similarity to several shots from You Only Live Twice is also apparent.
Kif's ability to climb walls is similar to that of several types of gecko.
Among the holographs who become rampant are Professor Moriarty, Attila the Hun, Jack the Ripper and an evil version of Abraham Lincoln. Professor Moriarty actually "came alive" in two episodes of Star Trek: The Next Generation while Jack the Ripper and Lincoln appeared in the Star Trek: The Original Series; "Evil Lincoln" is a specific reference to the episode "The Savage Curtain", where aliens pit some of history's most iconic heroes, including Lincoln, against history's most hated villains.
The sickbay scene is a parody of that from Star Trek: The Original Series, complete with sound effects. The sign references a creature from the series called a Horta, which gives severe acid burns. The sick bay's doctor is an obvious parody of Dr. Leonard "Bones" McCoy, and is named "Veins" in a deleted scene.
The planning calendar Amy is using is from August 3003 (August 3003 is the only month in 3003 to begin on a Monday)
At one point during the baby shower fry can be heard in the background saying "my face was stuck in a pizza"