Visible crew/equipment: Boom action is visible in reflections on computer consoles in the back, while Picard and LaForge talk to each other on the bridge. (00:40:15 - 00:40:46)
Visible crew/equipment: After the intro, when Garvin tells Gia to go home, Data is standing on the stairs and the actor's green mark is somewhat visible at Data's feet. This green T-mark is clearer when Data hands Garvin the radioactive box he's carrying. Then, when Garvin walks over to the table, there's an orange T-mark on the ground. (00:04:55 - 00:07:40)
Visible crew/equipment: After Gia tells Data to remove his hood, he asks how long it will be until Skoran and the others return. Then, when Data tells her that he must hurry he takes a step forward, and a green tape mark is visible on the floor. (00:36:35)
Gambit (2) - S7-E5
Other mistake: When the raiders' vessel fires on the Enterprise, only the starboard nacelle is hit. Right after the impact, Worf reports the port nacelle hit, then the starboard.
Character mistake: When Data and Picard discover Troi in her bathtub, Data scans her and comments that she is technically no longer "human." While Troi is indeed half human, she has the features of a Betazoid (black eyes and empathic abilities) and consistently describes herself and is described by others as a Betazoid. It is unusual for anyone to describe Troi as being "human", and it is unfathomable that Data would make that mistake.
Other mistake: When the ship is at max warp and Geordi states that at maximum warp the ship can only sustain two hours of emergency life support, Data, Troi and Worf are on the holodeck attempting to stop the train, but back in the bridge before they do you can see the view screen in the background and the bridge glass dome above Geordi, Picard and Riker that the ship is not moving at warp speed and is at standstill.
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.
Bloodlines - S7-E22
Visible crew/equipment: When Picard and his Jason have their "father and son" chat in the caves, you can see the mike shadow moving up and down a few times on Jason's leg. (00:33:20)
All Good Things... (2) - S7-E26
Visible crew/equipment: Captain Picard joins the poker game and Data asks the Captain if he wants to deal. Picard says "Thank you Mr. Data." Riker sits down, and just before Captain Picard starts saying "Actually..." a camera or other bit of equipment briefly pops into shot behind Riker.
Revealing mistake: When Data gives Spot his food, when he puts the food on the ground you can see his normal skin (human skin). (00:16:35)
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