Revealing mistake: In the scene where Barclay reappears on the transporter with the crewmember, they both fall to the ground. The transporter chief had put up a forcefield around the transporter chamber, in case something goes wrong. However, when the crewmember falls to the ground, his foot goes right through where the forcefield is meant to be. It is still active, as only a few seconds later we see it being deactivated.
Continuity mistake: 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).
Character mistake: At the end of the episode, after Lore has been defeated, Picard asks Data if he is O.K. Data replies, "I'm fine." One of the plot points of this episode is that Data cannot use contractions.
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)
Character mistake: In his exchange with Admiral McCoy, Data uses several contractions (i.e., shouldn't, I'm). For the rest of the series he doesn't, and in S3: Ep16, "The Offspring", he admits that his programming makes him incapable of using contractions. And in S4: Ep8, "Future Imperfect" Riker questions Data on when he started using contractions, knowing that Data is incapable of it.Movie Nut
Other mistake: When Q the Judge enters on his throne, at one point, the hydraulic arm the throne is on is visible, despite being black to blend in. Conversely, in "All Good Things...", the final episode, the arm is missing having been matted out by CGI techniques.Movie Nut