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."

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.'

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."

The current king of Jordan appeared briefly as an officer saluting Picard in one episode.

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.

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.

LeVar Burton is the only Star Trek cast-member to direct episodes in four Star Trek series.

The ceiling of the transporter chamber is actually the floor of the transporter chamber from the original series.

"VISOR" stands for Visual Instrument and Sensory Organ Replacement.

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.

Near the end of the episode, Picard and Crusher walk out of the cargo bay. As the doors close behind them, you can see Tasha Yar waving to the camera from inside the bay. Her character is killed in the next episode, but this one was filmed second. The actress was waving goodbye to all of her fans.

In this episode, Picard is studying Fermat's Great Theorem, and says it has remained unsolved for 800 years. Five years after the episode was made the theorem was proven, by Andrew Wiles and Richard Taylor from Princeton University (their proof is not the same as Fermat's though, as they used modern methods Fermat did not know of). In the Star Trek universe, this was referred to in an episode of Deep Space Nine, and is considered as a subtle correction for Picard's statements.

When Riker views Data's file on his computer, Data is listed as "NFN NMI Data." This stands for "no first name" and "no middle initial."

The test objects that O' Brien uses on the malfunctioning transporter are U.S. Navy sonar buoy transport cases.

Data's performance of Henry V was based, in part, on the 1989 film by Kenneth Branagh. In 1980, Patrick Stewart appeared in the TV movie Hamlet, Prince of Denmark with Derek Jacobi, who in turn appeared with Branagh in Henry V.

Gates McFadden (Commander Beverly Crusher, M.D) did all of her own stunts in this episode, while she was early on in her pregnancy.

The Federation flag has the Roman numeral MMCLXI, which is 2161, the year that the United Federation of Planets was founded. It's motto, "Ex astra, scientia" is latin for "from the stars, knowledge."

Because of guest star Leonard Nimoy's schedule, this episode was filmed before part one.

During a scene in Ten Forward with Wesley and Robin, in the background you can see a crew member in a blue uniform playing the game. This is actor Brent Spiner, minus his Data makeup.

Stephen Hawking guest stars in this episode, playing himself as a holodeck character (The "Poker with Einstein" program). This came about when he visited Paramount Pictures to promote "A Brief History of Time", and then told the Paramount people that he had always wanted to visit the Enterprise. He not only got to visit, but the writers added this special scene just so professor Hawking could appear on screen in a Star Trek episode. Hawking also reportedly stopped by the warp engine, smiled and said "I'm working on that".