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The Royale - S2-E12

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.

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Hero Worship - S5-E11

Continuity mistake: In the scene where Data is brushing Timothy's hair into a copy of his own hairstyle, he stops, kneels down and asks Timothy "Timothy, are you having bad dreams?" In this shot there is a big tuft of hair on the right side of Timothy's head that sticks straight out. When their conversation is over and Data stands up in the wider shot, all of Timothy's hair is in place.

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Descent (1) - S6-E26

Trivia: 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".

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Encounter at Farpoint (2) - S1-E2

Continuity mistake: When Picard tells Q in the final scene "Get off my ship." Q is standing to his right, and Picard has his head turned towards Q. But when the angle changes to show Q's response, Picard is standing facing Q directly, and without his head turned.

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Bloodlines - S7-E22

Audio problem: When Jason is having seizures in his quarters, Dr. Crusher gives him an injection to stop it. But watch Jason closely - he goes limp BEFORE you hear the sound of the hypospray.

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Bloodlines - S7-E22

Continuity mistake: When Jason and Picard are having a conversation in the holodeck, Jason says "I remember her telling me about all the boys and girls who didn't have anyone to care for them" while looking in the opposite direction of where Picard is sitting. The camera angle changes to a close-up and Jason now has his head turned slightly towards Picard.

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