The title is a humorous reference to the phrase "jumping the shark," an expression from Hollywood: Part 3 (1977) (where Fonzie water-skis over a shark), used to describe shows that have reached their peak and started to decline in quality. Chris Carter said that the title was tongue-in-cheek, and that it was their "way of lowering the boom on anybody who thought that it did."
The opening sequence, narrated by Morris Fletcher, reveals characters from the spin-off show The Lone Gunmen (2001) (Jimmy Bond and Yves Adele Harlow), but not featured in the X-Files series proper.
The name of character John Gillnitz is a portmanteau of the names of the episode's three writers: John Shiban, Vince Gilligan, and Frank Spotnitz.
One of the big jokes in the episode - that Morris Fletcher had a blueprint to a UFO that turned out to be for the Jupiter II spaceship in Lost in Space (1965) - took a lot of background wrangling to procure the rights to the design.