Visible crew/equipment: In Wesley's quarters, when the camera looks at Geordi, there appears to either be a person reflected on Wesley's device or a boom mike shadow plays across it.
Continuity mistake: When Yar is transported back to the ship her weapon was on her left arm. When on the transporter pad the weapon is on her right arm.
Continuity mistake: When Picard asks the Ferengi if they are withdrawing their surrender, Yar's arms pop back and forth from folded to extended as the shots change.
Where No One Has Gone Before - S1-E6
Visible crew/equipment: 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. [Not visible in the remastered Blu-ray version]. (00:06:00)
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)
Where No One Has Gone Before - S1-E6
Continuity mistake: Picard addresses the ballerina as ensign, when in fact she has no pips on her uniform, making her a crewman.
Where No One Has Gone Before - S1-E6
Other mistake: As the Enterprise comes out of warp in galaxy M33, the conference lounge is visible and is a re-use of the opening sequence. The movements of the people is identical.
Other mistake: As the ship approaches the energy cloud the second time, the registry number on the underside of the saucer is backwards.
Other mistake: As the Enterprise comes into the frame approaching the cloud, the registry numbers are reversed.
Plot hole: The entire premise of the episode is contradictory; the franchise makes abundantly clear through the so called Prime Directive that the Federation abides to a code (often creating moral dilemmas that may require to stretch the rules) that says that their staff is not supposed to interfere in world that haven't reached warp capabilities, nor involve themselves in their internal matters. In the first half of the episode, Riker and the others just go 'mingle' with the frisky natives without a care in the world, and yet in the second half the Prime Directive itself is referenced explicitly and it is part of the plot.
Suggested correction: They are just enjoying the hospitality of the planet's inhabitants. They are not interfering in their internal affairs or the development of their species. It's only when Wesley gets into trouble that the Prime Directive comes into play. The entire mission of The Enterprise is to make contact with other planets.
Even though they are supposed to make contact with other planets, it's pretty clear in the rest of the series after the first few episodes of Season 1 that they do not (intentionally) contact people that have no warp capability.
The Battle - S1-E9
Other mistake: When Capt. Picard gets beamed from The Stargazer back to The Enterprise at the end of the episode, he doesn't lower shields. Also, a Ferengi (DaiMan Bok) beams off the Stargazer onto his Ferengi ship earlier without lowering shields on the Stargazer. (00:35:45 - 00:44:20)
Hide and Q - S1-E10
Visible crew/equipment: When Riker, Dr. Crusher, and La Forge enter the area where the injured colonists are located, the mic is visible for a few seconds at top left of the shot.
Other mistake: When Deanna's mother arrives on the Enterprise, the sound of the transporter activating is heard. But the transporter technician is seen behind Picard and Deanna, and he remains standing by the wall with his arms behind his back. (00:09:00)
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 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)
Visible crew/equipment: When Riker tells Yar to open a channel to the Jarada, you can see the reflection of a boom mic in the workstation along the back wall behind him.
Other mistake: After greeting Crusher, Data explains where Picard is. Problem is he uses the contraction "he's" instead of "he is." Data is supposed to be incapable of this.
Suggested correction: This is only a mistake if the series is taken as a whole. At this point in the series, that particular trait wasn't part of the character. Data uses contractions multiple times in the first season, as the trait was added later.
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.
Continuity mistake: The lipstick on Picard changes between when he is kissed, and later when he leaves the holodeck (it's darker and on and above his lips.) Also, and more importantly, being holodeck matter, it should have disappeared after re-emerging in the real world.
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.
Continuity mistake: Near the end, after being subjected to the snowy scene, only Mr. Leech has snowflakes on him. They're on him as he steps into the corridor, then they're suddenly gone.
