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.
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.
Continuity mistake: In the opening sequence, the ship is positioned so that Shuttle Bay Two is aimed at the phenomena. But a moment later, the ship is facing into the stellar material.
Other mistake: As Guinan sits at the desk, she reaches toward, but doesn't touch, the control for the screen, but it activates.
Continuity mistake: As the ship fires the torpedoes, the familiar registry number on the underside of the saucer is completely missing.
Continuity mistake: Near the end of the episode, as they are preparing to beam down to the planet, Riker tells Warf to set his phaser on stun. He then holsters his own phaser and the transporter is activated. However, when they materialize on the planet, Riker is holding his phaser in his left hand.
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)
Other mistake: As Crusher enters the police station, Data says "Hiya, Doc. What's cookin?" He's supposed to be incapable of using contractions.
Revealing mistake: As Data looks at the information on Dixon Hill, as the computer flash feeds, you can see that it's all the same block of information starting with the title of the first novel, which is the title of the episode, "The Big Goodbye."
Visible crew/equipment: In the Medical center, as the camera pulls back from Picard, who is lying on the bio bed, the camera is reflected on the panels angled toward the camera.
Other mistake: As the Enterprise comes into the frame approaching the cloud, the registry numbers are reversed.
Where No One Has Gone Before - S1-E6
Other mistake: As the Enterprise comes out of warp in galaxy M33, the conference lounge is visible and is a re-use of the opening sequence. The movements of the people is identical.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Riker looks at the wooded scene on the holodeck, the water is flat calm, but when the camera looks at him, the water is noticeably more agitated before he gets to the rocks.
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