Picard utters "merde", the French word for "shit". As it was said in a foreign language, it passed the TV censors. Merde is sometimes translated as "damn" in subtitles. This is not euphemism but reflects common usage in French. French conversation is relaxed about the use of swearwords with sexual connotations, whose literal translations would be considered very strong or taboo in English. For example, "Je m'en fous" literally means "I don't give a f***" but is used by the French in the same way as the milder "I don't care."
Moriarty's use of the phrase "that dark fellow" in reference to Geordi/Watson is the only reference to a human's race or skin color ever made on TNG.
Although it is commonly believed that Sherlock Holmes has been in the public domain since sometime before the 1980s, the Sir Arthur Conan Doyle estate maintained copyright on the character - a claim set to expire in 2023 - until their claim was voided by a court ruling in 2013, ten years ahead of the planned date. Paramount Studios (producing company of the Star Trek franchise) obtained permission from the Doyles to make Das Geheimnis des verborgenen Tempels (1985) (acknowledged in that movie's end credits), but considered similar permission unnecessary for "Elementary, Dear Data," which they believed fell under the parody clause of copyright law, and thus aired the episode without notifying the Doyles. (ST:TNG producer Jeri Taylor, who joined the show in 1990, once incorrectly wrote that Paramount was wholly ignorant of the Doyles' property, but Doyle attorney Jon Lellenberg straightened this out.) The Doyles then wrote to Paramount that they were flattered by the episode, but felt it remained within their legal sphere, so they wanted in on any further Trek usage of their characters. Although Brent Spiner was eager to play Holmes again, nearly 4 years went by before Paramount and the Doyles agreed on a "reasonable licencing fee" for the sequel Ship in a Bottle (1993).
Geordi builds a model of HMS Victory, a sailing vessel of the Royal Navy launched in 1765, which in the real world is preserved in a dry dock in Portsmouth. Listed as part of the UK's National Historic Fleet, Victory has been the flagship of the First Sea Lord since October 2012. She is the oldest commissioned warship in the world and attracts around 350,000 visitors per year in her role as a museum ship.
Daniel Davis (Moriarty) later appeared in Jagd auf Roter Oktober (1990), portraying a senior crew member on the aircraft carrier USS Enterprise.