Zapp tells Kif to "get on the wing and pretend he's a gremlin". Zapp's character, especially his affect, is based on William Shatner's Captain James T. Kirk from Star Trek (1966). The gremlin remark is a reference to the Twilight Zone episode Nightmare at 20,000 Feet (1963), which also starred Shatner (before Star Trek), where there is indeed a gremlin on the wing. In the episode Shatner plays a man who has just recovered from a nervous breakdown, he is on a flight returning home after being released from a mental hospital when he looks out the window and sees some kind of monster on the wing trying to damage the engine. However no one else, including his wife, is able to see this "gremlin" which causes him to begin to question his sanity once again, his paranoia leads him to endanger everyone on the plane.
Zapp Brannigan's signature dots the 'i' with a heart.
In the cantina, one of the billiard balls is marked with the number e.
Leela says 'I don't want to put a rat in your face-cage, or whatever you kids say nowadays'. This refers to a horrific torture used to break the protagonist's spirit in the book '1984'; a torture that forced the man to betray the woman he loved.
Fry mentions a Barium shot, and the high price of one, in reference to a real life Barium shot, used to diagnose digestive cancers, and the high cost associated with them.