The "It is green" line Data says is a throwback to the same line Scotty says in Star Trek: By Any Other Name (1968) when describing a bottle of alcohol he had found and didn't know its proper brand name.
The writers did think about several characters from Star Trek (1966) TOS appearing in Relics before they settled on Scotty. Ronald D. Moore commented: "McCoy is old, Spock's playing James Bond on Romulus- and we couldn't do Kirk; it would raise too many other things. Nothing against the other characters, but Scotty seemed like the one with the most fun quotient."
A Dyson's Sphere is a real theory postulated by Freeman Dyson in 1959. But the actual sphere that Dyson theorized was not a solid object as seen in Relics. In an interview for the website Meaning of Life TV, Dyson himself was asked if he had known that a Dyson Sphere was featured on the show and mentioned specifically by name, to which he replied he was aware of it because his daughter had sent him a taped copy of this episode. He went on to say that the episode was "fun to watch, and even though it was all nonsense, it was still quite a good piece of cinema."
The scene of the original Enterprise was made by looping footage of the empty bridge seen in Star Trek: This Side of Paradise (1967), and bluescreening it behind James Doohan. Because of this, only small parts of the set had to be built. Ironically, Doohan didn't appear in the episode the shot was taken from. The shot of the original viewscreen was recycled from Star Trek: The Mark of Gideon (1969).
In the original script, Scotty conversed with holograms of the crew of the first Enterprise, by using clips from Star Trek (1966): The Original Series. It had to be cut for budgetary reasons, but it does appear in the novelization. Picard even takes part in it for a while. The producers did eventually get to combine TOS footage with a present-day story in the Deep Space Nine episode Star Trek: Deep Space Nine: Trials and Tribble-ations (1996).
A novelization was written around this episode. It expands upon a few things like the holodeck scene, where not only does Scotty recreate the bridge of the Enterprise, but the crew as well, back in their heyday. We also see something of Scotty's life 75 years ago aboard the Jenolan, where he strikes up a friendship with Matt Franklin, the man who goes into transporter limbo with Scotty. The officer who shows Scotty his new quarters has a bigger role, too, in a subplot where he doesn't get along at all with Riker, and even assumes that showing Scotty his quarters must be a punishment from Riker.
When Scotty walks onto the Holodeck, there is a red alert light that wasn't a part of the bridge all those years ago. When filming "Relics", the set designers removed the dedication plaque from the turbolift foyer to create the illusion of a different part of the bridge and save money on building more of the set.
Whoopi Goldberg was asked to return to her occasional role as Guinan the bartender, but her schedule didn't mesh with the timing of this episode's production, so Data fills in as the Ten Forward bartender instead.
The USS Jenolan was named after the Jenolan Caves, which writer Ronald D. Moore had visited while he was in Sydney, Australia for a Star Trek (1966) convention. The city provided the starship's "Sydney class" designation.
A close-up of Scotty's hand on a control panel was actually a shot of another person's hand. Actor James Doohan, who plays Scotty, lost his right middle finger during the World War II D-Day invasion of Normandy. (Several quick shots throughout the original series and the first six Trek films reveal this.)
The trivia items below may give away important plot points.
A scene between Mr. Scott and Deanna Troi was filmed but cut because of the length of the episode. It was to have occurred after Scott had his blow-up with Geordi La Forge in Engineering and just before his visit to Ten-Forward where he and Data have the "it's green" conversation. Deanna tried to help Scott deal with his feeling of being out of place in the 24th century, although he resisted her entreaties - but it explains why he gives Deanna a kiss in the final scene, in what otherwise appears to be her only appearance in this episode.
In the beginning of this episode, Captain Montgomery Scott exclaims in response to learning he has met with The Enterprise crew, saying "The Enterprise, I should ha' known. I bet Jim Kirk himself hauled the old gal out of moth balls to come lookin' for me". This will lead to a continuity problem with the movie Star Trek: Generations (1994), where Captain Scott was present at the supposed death of Kirk on the Enterprise-B. This was due to Scotty in the movie being a last minute substitution for Spock when Leonard Nimoy was not available for the part. (It could be argued that he was not fully conscious due to his memory capacities not being restored to full function when he's first seen in this episode.)