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: When commander Data is reciting the code to lock the rest of the crew out of the computer, he states the code '1-7-3-4-6-7-3-2-1-4-7-6-C-3-2-7-8-9-7-7-7-6-4-3-T-7-3-2-V-7-3-1-1-7-8-8-8-7-3-2-4-7-6-7-8-9-7-6-4-3-7-6-LOCK', but when the computer screen is shown the code reads '1-7-3-4-6-7-2-1-4-7-6-C-3-2-7-8-9-7-7-7-6-3-T-7-3-2-V-7-3-1-1-7-1-8-8-8-7-3-2-4-7-6-7-8-9-7-6-4-3-7-6-LOCK.'
Who Watches The Watchers - S3-E4
Revealing mistake: About 38 minutes into the show, when Dr. Mary Warren dies and there's a close up of Picard & Nuria, you can see the her hand moving up and down as she breathes.
Continuity mistake: In the reality where Worf and Troi are married, when she kisses his neck, all of Worf's hair has been pulled back behind his head. When he gets up and turns to face her, the hair on the right side of his head is draped over his shoulder. When the camera angle changes and Worf turns to face it, his hair is pulled back behind his head again. (It isn't Worf changing dimensions again, because he doesn't have the moment of weakness before it happens that he has through the rest of the episode.). (00:23:05)
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.
Continuity mistake: In one scene on the planet, Riker's clone is lying under a table fixing something and Riker is sitting in a chair talking to him. There are two camera angles used. In one angle when the clone is talking and a body double is sitting in the chair he is facing directly towards the table but in the other camera angle where you can only see Riker, the chair is at an angle facing towards where his clone is lying on the floor.
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)
Visible crew/equipment: A boom Mic is visible about nine minutes in, just as Riker and Picard begin walking down the corridor talking about Lwaxana Troi getting married aboard the enterprise.
Continuity mistake: Looking at the shuttlecraft while sitting in the shuttle bay and after it has departed the Enterprise, you can tell they are different types of shuttles. The one in the shuttle bay has more angular lines with straight edges. The one outside the Enterprise has more curves than angles to its lines.
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.
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.
Plot hole: The binars needed two people to upload the data back to their world but they only intended on keeping Riker in the holodeck. Riker is just one person. Picard came into the holodeck purely by accident - even Minuet said this was true. If Picard hadn't been there, Riker could not have uploaded the data on his own and the binars' plan would have failed.
Suggested correction: The Binars only trapped Riker because they thought they might need someone to restore the computer for them, which wouldn't have taken 2 Enterprise crew members. It was the fact that the Binars got to their planet too late that required Picard and Riker to work together. However, the Binars already knew Picard was on the Holodeck before they initiated their plan because when Picard exits his ready room he says he's going to join Riker. Had Picard not done this, certainly the Binars could have kept a 2nd crew member on-board somehow, if needed.
Conspiracy - S1-E25
Revealing mistake: After the fight with Riker, Quinn throws Worf through the room, hitting a wall. The replicator part of the wall moves.
Visible crew/equipment: Numerous times in the bridge scenes, the studio lighting rigs are seen in reflections on the work station screens.
Other mistake: After the report that Picard is close to death, the scene shifts to a close up of La Forge's hand turning on controls. If you look closely, you can see that both panels are re-purposed CANX-23429 remote control units. The markings are for volume, radio, transmitter, receiver, phone jacks and a microphone jack.
Other mistake: When Data is interpreting between Captain Picard and Riva, he uses signs for words Captain Picard has not yet spoken, and voices concepts before Riva has signed them. He also doesn't interpret everything the Captain and counselor Troi say.
Continuity mistake: When the original Picard shoots the duplicate Picard with a phaser in the shuttlebay, he shoots him square in the chest. But in later shots, the scorch marks from the phaser are on his abdomen area.
The Pegasus - S7-E12
Continuity mistake: In the opening log entry of the first episode, Picard says that "I have been informed that a highly experienced man, one Commander William Riker..." He sounds as though he has been assigned a First Officer without knowing him. However, in this episode he tells Pressman that he read Riker's file, and wanted him, based on Riker's adamant refusal to obey an order that went against his safety protocol.
Suggested correction: There's no error here. Picard likely read the files of many officers and requested the ones he preferred, and Star Fleet informed him which one he would get.
Continuity mistake: With his right arm Data is accessing the holodeck circuitry via the manhole while he is holding back a taxi cab with his left arm. Each time the scene switches to viewing Data from the back you see his right hand in the manhole and eventually his left hand appears. All the while you still hear the sound of the taxi cab. Each time the scene shows Data from the front he is holding back the taxi cab with his left hand.
Visible crew/equipment: In the opening scene, just before Picard comes out of his room, you can see the shadow of the boom microphone.
