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
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
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
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.
Chosen answer: The uniform does indeed change colour. It may be due to the need for a green screen in part, or perhaps some lighting altering our perception. That being said, it certainly looks green at the start, blue thereafter.
The show has been done in HD now and not sure if they fix this problem.
Dan23