Visible crew/equipment: In the episode "Reunification part 2" when Picard, Spock, and Data have just escaped from the female Romulan commander, when they are walking out of the room look at the green glass ornament - you can see reflection of a crew member.

Visible crew/equipment: In the episode "where no-one has gone before" from series 1, near the start, just as Riker says "you have all the time you need", the engine consultant stops and turns around. As he does so, look above his head and you can see a microphone hanging down. The camera quickly adjusts so it's not visible any more.

Continuity: In the episode 'Yesterday's Enterprise' (season three, episode 15), watch the final scene with Geordi and Guinan in Ten-Forward. Although time and the universe has returned to normal, Geordi is still wearing the uniform from the alternate timeline (note the sleeve detail, and the extended neck piece).

Revealing: In season 5, "The Game," the brainwashed crew members hold Wesley's eyes open to force him to see the mind-controlling game. Their intention is to prevent him from closing his eyes, which would protect him from the device. While they are doing this, he blinks.

Continuity: Picard addresses the ballerina as ensign, when in fact she has no pips on her uniform, making her a crewman.

Continuity: The creators re-did the titles from the third season on, but only from before the shot of the ringed planet, and they didn't make sure they matched. Compare the movement of the stars inside the rings and the star field outside the rings - they move in different directions compared to each other.