Other mistake: As Troi describes her idea of "real" chocolate to the computer, it interrupts her with a warning about the nutritional value of her request. The reply is in two parts, and between the parts, you hear the intake of breath, something no computer would do.
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.
Other mistake: While Riker looks over Data's shoulder, the make up on Data's eyebrows is incomplete. The left is lighter, the right is darker.
Other mistake: In this episode, in Riker's memory, the encounter between him and Quinn is re-lived. As Quinn starts to attack Riker, you can see Riker's stunt double's face, and tell that it's Quinn's stunt double, as the hair is smooth, not styled. Also, Riker is a few inches taller than Quinn, but in the onset of the attack, they're equal heights.
Data's Day - S4-E11
Revealing mistake: When Data and Dr. Crusher are tap dancing on the holodeck, whenever the camera angle changes to a wide shot from above (for the more complex dance moves), it's clear it is not Brent Spiner but a stand-in dancing.
Continuity mistake: When alien party arrives, the turbaned assistant puts down the carpet roll the wrong way round. The next shot it is miraculously switched around so it can be rolled out towards Picard.
Continuity mistake: After Pulaski examines Riker's leg, and readies to beam up, he leans to the right to get up. In the wide shot, he does it again.
Revealing mistake: As Data cautions La Forge not to say anything, his actual flesh tone is visible on his palm.
Conspiracy - S1-E25
Continuity mistake: After leaving the table in headquarters, Picard meets Riker at the door. In the far shots, Picard has his back to the table. In the close up, his left shoulder is towards the table.
Continuity mistake: William Riker is playing cards with La Forge and Worf. The camera is focusing on Riker and there is no 4th chair. When Tom Riker enters, William says "Why don't you join us" and now removes his trombone from the 4th chair which has suddenly appeared. (00:31:25)
The Arsenal of Freedom - S1-E21
Continuity mistake: As the Enterprise is attacked, the registry number is reversed.
Visible crew/equipment: After Picard, Troi, and Worf have beamed down to the planet to meet Riva, when Harmony asks if they need food or refreshments, just as Picards says, "Thank you, no," a crewmember's elbow can be seen at the left side of the screen (this one is not visible on the Netflix version). Then when Troi says, "Your method of communication is elegant and quite beautiful," a crewmember (likely the same one as earlier) can be seen at the left side of the screen. (00:07:20 - 00:10:40)
Yesterday's Enterprise - S3-E15
Other mistake: The Klingons ordering the Enterprise to prepare for boarding parties doesn't make sense. La Forge had announced only moments earlier that the Enterprise was on the verge of a warp core breach. The Klingons' ship's sensors should have been able to detect the Enterprise's impending destruction.
Conspiracy - S1-E25
Other mistake: When Riker is knocked into the glass table, he should have been bleeding from the impact, but when the close up shows him unconscious, he is not.
Revealing mistake: When the first villain hits Worf with the chair, just as Alexander is yelling "look out", you can tell it is a stunt double.
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.
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)
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?