When Ray is singing and dancing around on the ship, it is a scene-for-scene of Arrested Development Jessica Walter in Spring Breakout (2005).
When Archer and Malory (as Funbeak) are escaping, Malory says they need a distraction, to which Archer responds, "You could do your bird dance". This is in reference to Arrested Development (2003) and the Bluth family bird dances. Archer: "You could do your bird dance." Malory: "You're one to talk!" Archer: "How?" Malory: "Exactly."
Pam carrying Krieger (in pieces) on her back while the crew is escaping is an homage reference to Chewbacca carrying C3-PO during a similar escape run from Cloud City in Star Wars: Episode V - The Empire Strikes Back (1980).
When the crew is deciding who is going to fight whom, Kreiger says he literally can't. This is due to Isaac Asimov's Three Laws of Robots. (The first law is that a robot shall not harm a human, or by inaction allow a human to come to harm. The second law is that a robot shall obey any instruction given to it by a human, except one that would cause it to violate the First Law, and the third law is that a robot shall avoid actions or situations that could cause it to come to harm itself, unless avoiding said action or situation would lead to violation of the First or Second Law.)
The escape ship has an emblem of the Polish Air Forces on its seats.