Trivia: 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.
Trivia: 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.
Trivia: 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 what appears to be a Vulcan nerve pinch (although in the script it is referred to as a "carotid artery block"), 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.
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.
Trivia: 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.