Other mistake: When Picard walks into the brig to talk to Q, something falls in the doorway and Picard almost kicks it with his foot. The door then closes on the item that fell. (00:11:20)
Continuity mistake: Near the end, when Pulaski finally stops the infection in Riker and is just about to contact Picard with her success, look at Riker lying on the table. His eyes are open, then he closes them slowly. The next scene has Riker opening his eyes for the first time after recovering from the procedure.
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)
Continuity mistake: When Data bends the bar, he does so much that the sides are almost parallel with a very acute angle. When Riker puts it on the desk, it's much more curved and the sides aren't as parallel anymore.
Continuity mistake: Data's insignia pips are backwards in the first scene as he is talking to Picard on the bridge.
When The Bough Breaks - S1-E17
Visible crew/equipment: When Data and Geordi come up to address Picard, there are two lines of tape on the floor for positions.
Visible crew/equipment: As Picard goes to sit in his seat, there's a shadow of the boom mike playing across the wall above Burke and Kolrami's heads.
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