Trivia: Another joke from the set designers: whenever someone is in the Jeffries Tubes, you will see several pipes on the walls labeled "GNDN" this stands for "Goes Nowhere, Does Nothing."
Trivia: The cast really are very good friends. At LeVar Burton's wedding in 1992, the best man was Brent Spiner and the ushers were Patrick Stewart, Jonathan Frakes and Michael Dorn. And when Brent Spiner recorded an album (Ol' Yellow Eyes is Back), the backing groups listed as The Sunspots are again the male members of the bridge crew.
Trivia: The ceiling of the transporter chamber is actually the floor of the transporter chamber from the original series.
Trivia: Further to the Trivia entry, a control in Engineering is labelled 'Infinite Improbability Drive' as a nod to Douglas Adams' Hitchhiker's Guide To The Galaxy. Also, one of the indicators above a diagnostic bed in Sickbay reads 'Medical Insurance Remaining.'
Trivia: The transporter was first created by Gene Roddenberry in 1966 for the original Star Trek, as an easier (and cheaper) alternative to get members of the Enterprise crew onto a planet's surface, instead of having the ship land on the planet each time. The same holds true here. Even the original version was based on a similar effect in the movie Forbidden Planet.
Trivia: The set designers added in small jokes everywhere. On the cross section of the ship near the tactical station, there are small objects in the picture that do not show up on television. (There are mice in the halls, cars in the cargo bay, a duck in a hall and a hypodermic needle in sickbay). In the halls, the red strips labeling the compartments say things like "3 hundred thousand kilometers per second, it's not just a good idea, it's the law, your mileage may vary of course", "Objects in mirror are closer than they appear to be", "A stitch in time saves nine", "In space, no one can hear you scream", and "Don't step on Superman's cape."
Trivia: A constant question during the run of all the Trek series is why Klingons look so much different, from "Star Trek: The Motion Picture" on, than they did in the original series. The real reason is the movies and later TV series had a better makeup budget. However, the "Star Trek: Enterprise" episodes "Affliction" and "Divergence" provide a canon answer. Klingons acquired genetically engineered human embryos left over from Earth's Eugenic Wars and used them to augment their soldiers. It worked but created a virus that threatened to annihilate the Klingon race. Dr. Phlox and a Klingon doctor found a cure, but it resulted in all Klingons becoming far more human in appearance. Sometime between these episodes and the first Trek movie, a cure was found, returning the Klingons to their present day "ridged-head" appearance.
Trivia: The transporter system in the Star Trek universe uses a Heisenberg compensator. This is to counter Heisenberg's Uncertainty Principle, which pretty much eliminated the potential for transporters, given Heisenberg's assertion that it would be impossible to re-assemble all the components of an item transported.
Trivia: Starting in season 4, the number "47" appears in the dialog of several episodes (from station numbers to codes to percentages). This comes from one of the executive story editor and writer, Joe Manosky (who joined TNG in season 4). Manosky was in a club during college called "The 47 Society" and the number was written in as an inside joke. It carried its way through Voyager, DS9, and films. Writer and producer, Rick Berman, once joked "47 is 42 corrected for inflation."
Trivia: Most of the time when the crew plays poker, they do what's known as "string betting", Riker is especially notorious for doing this. String betting is calling the current bet and then raising in the same turn. It's not allowed in most poker games. You either call or raise (or fold) but not both. Since this is the future (where rules can change) and they're friendly games, it's more a point of trivia than a mistake. But can still be cringeworthy to watch.
Trivia: During the series, a number of times the shot of the Enterprise moving toward the destination at Impulse power is re-used, and there is a figure moving from left to right along the Conference room windows. According to the LCARSCom.net website, the figure in question is Captain Picard.