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.
Revealing mistake: In the cargo bay, as Riker stands alone, through the whole scene where a case is about to hit him, you can tell it's a stuntman with a bad wig.
Continuity mistake: As Geordi talks to Ms. Rogers, Riker is walking in the background by some containers and a crewman in blue. After a cut to Ms. Rogers, Riker is suddenly alone with a data pad.
Descent (1) - S6-E26
Revealing mistake: In the hand-to-hand with the Borg soldier, Data's stunt double is easily identifiable.
Audio problem: We hear Reva's female member of his choir say "I have been expecting you", but her mouth doesn't move.
Continuity mistake: As Q approaches Picard and Riker's position while playing a trumpet, both of Q's hands are on the horn. A second later, his left hand is down by his side. Then, after he makes cigars appear in Picard and Riker's mouths, his left hand is extended as he says the first part of his lines. A second later, both hands are on his horn.
Continuity mistake: As Worf goes to enter the portal to the Enterprise carrying Data, his right hand is free, and his left is holding Data's left hand. Appearing on the bridge, Worf's left hand is on Data's leg, his right hand on Data's wrist.
Where Silence Has Lease - S2-E2
Visible crew/equipment: As Picard approaches Data's position, the boom mic is reflected on the panel behind him.
Continuity mistake: When Wesley Crusher and his school chum accidentally hit Picard with a snowball from the holodeck doorway, it makes a huge wet spot on the captain's left shoulder. However, when Picard tells them "Don't let it happen again," as he turns to walk away, the wet spot is now suddenly dry. (00:36:00)
Devil's Due - S4-E13
Continuity mistake: In Picard's quarters, Ardra appears as Troi. After reappearing as herself, she puts her hands on her hips. After the angle change, she repeats the motion.
Continuity mistake: When talking to Ral, Riker takes a sip of his drink, sets the glass down, and clasps his hands. A second later, he repeats clasping his hands.
Factual error: When the starboard nacelle causes the ship to spin, the view of the stars on the main screen on the bridge should move toward the right side of the screen, rather than standing still.
We'll Always Have Paris - S1-E24
Continuity mistake: The red towel Picard holds goes from draped over the front of the arm rest, to over his hand between angles.
Continuity mistake: When the Enterprise activates the deflector dish, there are four points emitting beams. However, there are five beams emitting after the angle changes.
Other mistake: After the signal change to a continuous output, the Crystalline Entity vibrates. As it does, look at the background stars. They also vibrate in time with the Entity, although the signal is focused on Entity alone.
Continuity mistake: When Picard looks down the mountain to look at the town he has a straw hat in his left hand, next shot it's gone.
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