Continuity mistake: 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.
Continuity mistake: The view of the starfield in the ship's windows is always inconsistent whenever they are orbiting a planet. Sometimes the stars appear to be moving by, and sometimes they are completely static.
Continuity mistake: In the early episodes, Geordi's rank is inconsistent. In "Encounter at Farpoint", he is a full lieutenant. In subsequent episodes, he is a lieutenant junior grade, before being promoted back to full lieutenant.
Visible crew/equipment: Numerous times in the bridge scenes, the studio lighting rigs are seen in reflections on the work station screens.
Continuity mistake: In the Engine Room, after Geordi calls Wesley and Data, Wes turns around and drops his hands. In the next shot, his hands are back up in front of him.
Suggested correction: Which episode is this for?
Visible crew/equipment: Numerous times throughout the series, the screws that hold on the panel faces on the Conn and Ops positions are visible.
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)
Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
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)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Q comes into the courtroom on his floating dais, he goes to his right and gestures to the people to sit. He then starts to his left, and puts his hand down. After the angle cuts to Picard's point of view, as Q goes left his hand is dropping to the arm rest again. (00:21:35)
Encounter at Farpoint (1) - S1-E1
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. (00:21:45)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: The court announcer and the bell ringer bow respectively, and Q starts to depart. From Q's point of view, they start to bow again. (00:29:55)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: Commander Data tells Picard the Saucer Section will arrive in 51 minutes. Riker's synopsis audio can be heard in the background without interruption, and shortly after Data says this, the cameras turn back to Riker and the Video synopsis ends. Riker immediately reports to Picard who then receives the message that the Saucer Section is in orbit. Now, Riker was watching highlights of video footage from the Bridge, of which we see almost all of it because there really wouldn't be that much to view. And that's really all he could watch since we don't have cameras in the "Q-verse" and we see the footage ending with the Q sphere chasing the ship. Also, the entire ordeal was far less than an hour so there's no way a highlight reel could take an hour, not to mention the uninterrupted audio. We seem to be missing almost an entire hour. (00:37:32)
Encounter at Farpoint (1) - S1-E1
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.
Suggested correction: It is true that in later seasons he is unable to use contractions. However, since that characteristic was not introduced in the first season, this is not a mistake. His behavior is consistent with the character's behavior throughout the first season.
It's still a possible mistake, even if it wasn't part of season 1 scripting. Just because we only learn later that Data doesn't use contractions, doesn't make this mistake invalid. We learn Data was specifically constructed that way and hadn't been able to use contraction since being created, which means all of season 1 he shouldn't be using contractions. 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.
Incorrect. It would be a mistake if he used a contraction after the trait was added to his character, but the mistake can't be retroactive as it wasn't a mistake for him to use it at that point in the show.
Encounter at Farpoint (1) - S1-E1
Other mistake: As the Enterprise is fleeing from Q, it peaks around Warp 9.6 which according to the fact books, translates to around 1000c in sidereal space. Also according to the fact books, the saucer section is not capable of sustained Warp flight on its own. Also, at the beginning of The Chase scene, the Enterprise is on course to Farpoint, Q's fence is perpendicular to it. The Enterprise does at least a 90°+ turn beginning her escape maneuver prior to separation, so it is definitely not flying past Farpoint during The Chase. Still the saucer section somehow makes it to Farpoint a mere 51 minutes after the engine section. There's no evidence at all in the dialog that it was Q's doing.
Encounter at Farpoint (1) - S1-E1
Other mistake: As the Enterprise starts to turn to starboard (right) to escape the energy field Q set up, as the field is moving to port (left, indicating the ship is turning right) the starfield is also moving right, when it should be moving left.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Riker looks at the wooded scene on the holodeck, the water is flat calm, but when the camera looks at him, the water is noticeably more agitated before he gets to the rocks.
Encounter at Farpoint (1) - S1-E1
Visible crew/equipment: As Zorn leans over his desk after Riker leaves, the studio light is reflected on the monitor screen to his left.
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.
Encounter at Farpoint (2) - S1-E2
Continuity mistake: The computer is directing Commander Riker toward L.C. Data in holodeck area 4-J. As he walks along the corridor the computer helps him by saying that he should go to "the next hatchway on your right." Then Riker turns left (according to the way he was going) to enter the holodeck.