Mulder is Chris Carter's mother's maiden name. Mulder's first name, Fox, is the name of Carter's childhood friend. Scully is the name of the LA Dodgers' sports announcer Vin Scully, to whom Carter listened as a child. In episode #6.19, The Unnatural, the voice announcing the Dodgers game is none other than Vin Scully.
The name of the Negro League Team "Roswell Grays" is a play on words. Roswell Gray also refers to the type of alien typically portrayed in movies/TV that people allegedly claim to see (gray skin, big eyes, small mouth, no nose.)
At the end of the opening credits where the quote "THE TRUTH IS OUT THERE" usually is, the quote is "IN THE BIG INNING" and is word play for 'in the beginning' as this episode takes place in Roswell, NM in 1947: when and where modern day alien scientist and UFOlogists began alien conspiracy theories/work due to the Roswell Incident of 1947.
First episode where a alien bounty hunter has a conversation with a character. Most instances (up to this episode) when alien bounty hunters have screen time they are silent and carry out their missions.
It appears the name of this show is a play on the title of the 1984 Robert Redford movie "The Natural", in which a virtually unknown ball player comes out of nowhere to become a legendary player with an almost divine talent.
Fredric Lehne, who plays young Arthur Dales, was also in a few episodes of season 2 and 6 in Supernatural as the yellow-eyed demon Azazel. Supernatural also constantly makes references to the X-Files and this particular episode is called "The Unnatural" which could be another way of saying "supernatural".
The trivia item below may give away important plot points.
Episode ends with Mulder teaching Scully playing baseball. He asks her if she has ever played baseball, and she probably lies to him in order to flirt with him, as far as she grow up with two brothers and her mother told Mulder she used to be a tomboy.