This episode, airing in 1988, predicts that Fermat's Last Theorem would have gone unsolved for 800 years as of the mid-24th century. It was actually solved in 1993 by Princeton University Professor Andrew Wiles. In 2016 he won the Abel prize in recognition of his accomplishment.
The Royale book begins, "It was a dark and stormy night." This opening line was first used in 1830 by Sir Edward George Bulwer-Lytton for the novel Paul Clifford, and has been imitated and spoofed by countless other authors including W.W. Jacobs and Charles M. Schulz. It is often used to make fun of humorously incompetent or overly melodramatic writing, which is why Picard says that it's not a very promising start. San Jose State University holds an annual Bulwer-Lytton Fiction Contest, in which entrants are encouraged to come up with equally humorously incompetent opening sentences.
There was a Colonel Richard "Stephen" Ritchie in the U.S. Air Force. He was the first and only Air Force Ace pilot in the Vietnam War. He retired a highly decorated Brigadier General in 1999 and as of 2016 is still alive and well and gives speeches on his free time.
The trivia item below may give away important plot points.
In the original final draft script, Major Richey's image was kept alive in the casino by the aliens, and a dead away team crew woman was retained to keep him company after the unseen casino manager told the story of the Colonel's shipwreck; Richey was the only member of a seven-person crew to survive. None of this made it into the final script or the finished episode.