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.
Audio problem: When Riker leaves Deanna and Wyatt at the holodeck you hear the door. You don't hear it a minute ago, when Wyatt enters the holodeck - he just appears. (00:27:30 - 00:28:15)
Continuity mistake: When Data brings up a picture of the original Kirk-era Enterprise in conjunction with the log talking about the water-intoxicant, the picture is of the refitted movie-style Enterprise - not the original round-nacelled model that was involved in the events of "The Naked Time."
Continuity mistake: After entering the Holodeck for the 2nd time, a vendor hands a folded piece of paper to Picard, yet Picard receives it unfolded.
Conspiracy - S1-E25
Revealing mistake: As Riker swings on Quinn, and a moment later, tossed onto a glass table, both times it can be seen that it's Riker's stunt double.
Revealing mistake: When Data sits in his post, his neck pips are black and then gold. In the next jump scene when he is in the back of the bridge with his commanders, the pips are reversed.
Visible crew/equipment: When Yar and Worf prepare to cut through the wall beneath the capital city, you can see the flash-powder cord before they shoot and the phaser beams get F/X'd in.
Continuity mistake: While Troi and Yar are talking while holding hands in Troi's quarters, there is a piece of cloth between their hands in one camera angle, but in another camera angle, there is nothing between their hands.
Continuity mistake: Several episodes have stardates after this episode, but still have Tasha Yar in them (even though she dies in this episode). They aired before this episode. The series producers later formalized their stardate system so that they take place in the order the episodes air.
Revealing mistake: As Riker is being dragged toward Armus, the wire pulling him can be seen disturbing the sand and the surface of the slime pool.
We'll Always Have Paris - S1-E24
Character mistake: When Data is on the planet, about to drop the material into the temporal rift, one of the three Datas asks which one of them should do it. The middle Data replies, "Me. It's me." Data is meant to be incapable of using a contraction.
Suggested correction: That character trait was not established until season 2. Data uses contractions multiple times in the first season.
While it was explicitly expressed in season 2 that Data can not use contractions, the fact that they did established this character trait means it could be a valid mistake since the trait is meant to show Data could never use contractions since his creation, not that he suddenly developed it some 30-odd years later. Although it would probably be best to submit it as a mistake in season 2 when it's mentioned that it contradicts what was established or at least make one character mistake for "all of season 1" than list every individual time it happened.
Where No One Has Gone Before - S1-E6
Character mistake: Mr. Kosinski is trying to explain what happened to allow them to travel so far. He says, "I applied the energy asymptomatically", when he meant "asymptotically." (The subtitles for this scene are correct). (00:13:50)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: While trying to escape Q, the Enterprise fires eight torpedoes, but only five explode. If all detonated, the last three weren't shown, but Tasha reported detonation after only five. (00:15:30 - 00:17:10)
Plot hole: The crew makes no attempt to re-board the Enterprise or stop it from leaving the starbase even after they find out there is no danger from the anti-matter.
Continuity mistake: When the away team encounters the evil oily blob thing, it makes their equipment fly away. Later they have apparently recovered it. But strange things keep happening to Geordi's weapon: when he and the others run forward to rescue Riker, Geordi accidentally drops it in the black pool when he stops abruptly. Admittedly, you can't prove that's a mistake even though it has no purpose in the story. But shortly afterwards the phaser is back on Geordi's belt, clean. Did the sticky, malicious, bullying blob give it back just like that? (People often try and find justifications for mistakes, but in this case, wishful thinking can only give us an extremely unlikely explanation.)
Continuity mistake: When the two holographic villains are disintegrating outside the holodeck, there is a corridor opposite the holodeck. When the good guys exit a minute later, there is suddenly a solid wall. (00:38:20 - 00:39:20)
Encounter at Farpoint (1) - S1-E1
Visible crew/equipment: On the very beginning of the second shot of the episode (the shot in engineering showing Picard walking around), the camera seems to shake or wobble. It's pretty obvious that the camera must have hit a part of the set or was bumped by a crew member. (00:02:45)
When The Bough Breaks - S1-E17
Audio problem: Riker's lips don't match what he is saying when we hear Riker's statement of being surprised when Tasha hasn't heard of the stories of Aldea.
Continuity mistake: Watch when Geordi on the bridge calls up Dr. Crusher in Sick Bay. There's a white-haired medical assistant working on someone behind Geordi. Then when Dr. Crusher responds to Geordi's page, the same assistant is down in Sick Bay with her. Then they cut back to Geordi and the assistant is back up on the bridge again.
When The Bough Breaks - S1-E17
Continuity mistake: When Wesley is being introduced to the Companion, the camera zooms in to see the entire console up on the full screen with NO hands on it, but when it cuts to a side view, Radue's wife's hands are on the console.
