Closed captioning, in its infancy in the 80s, often dropped words and letters by accident. In the original broadcast of this episode, the captioning of Riva's line, "We could dine together," lost an N, resulting in a rather bizarre exchange. Riva: We could die together. Troi: I'd like that.
Early on in the episode, just after Picard realises what the terrorists are up to. He fights and disables one of the terrorists, a human played by Tim Russ, using a Vulcan Nerve Pinch, which he learned from Sarek in an earlier episode. It's ironic that Tim Russ would later go on to play the Vulcan Lt. Tuvok on Voyager, and use that very same move on many an occasion.
In this episode, the stripe on Picard's door is light purple. Usually, the info stripes are brown with white lettering. Also, you see that Picard's quarters are on Deck 9, and has a view of space, whereas Kirk's cabin was further inside, with no windows. This was a means of protecting him from attack.
When Captain Picard is reading Hotel Royale in his ready room, he comments that the book's first line, 'it was a dark and stormy night', is "not a promising beginning". This line is actually the first line of Edward Bulwer-Lytton's Paul Clifford; the line has become so clichéd that it frequently appears in satirical works to denote humorously incompetent or overly melodramatic writing.
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".
The current King of Jordan appeared briefly as an officer saluting Picard in one episode.
"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.
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."