Revealing mistake: In the corridor, as Wesley faces the Zaldan, the hallway behind the scene is obviously a painting due to the shadow of the support on the edges.
Visible crew/equipment: As La Forge and Crusher leave the bridge, and the camera closes in on Riker, there's a shadow of a piece of filming equipment on the wall behind and to the left of his head, at the upper right of the shot.
Other mistake: As the cloaked Warbird looks at the Enterprise, the registry number on the under side of the saucer is reversed.
Conspiracy - S1-E25
Continuity mistake: As the ship enters Sector 63, there's a shot of the Conn and Ops positions and the screen. Geordi is in the right chair, the left is empty. Data is nowhere on the bridge, but when as Picard walks forward, Data's arm is suddenly in position.
Visible crew/equipment: As Picard walks past the display of the ship the lighting rigs, camera and sound equipment are reflected in the panels.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: The court announcer and the bell ringer bow respectively, and Q starts to depart. From Q's point of view, they start to bow again. (00:29:55)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Q comes into the courtroom on his floating dais, he goes to his right and gestures to the people to sit. He then starts to his left, and puts his hand down. After the angle cuts to Picard's point of view, as Q goes left his hand is dropping to the arm rest again. (00:21:35)
Character mistake: When the artifacts from the late 19th century, found in a cave, are identified by the away team, Data identifies the pistol as a "double action" Colt 45, circa 1873. The pistol is a Colt single action army, caliber .45. Certainly not a "double action".
Devil's Due - S4-E13
Continuity mistake: As the camera does a close up on the shuttle craft's forward window as it approaches the Enterprise, the dorsal section is seen getting larger the closer they get. As Data and Picard talk, the image fades out, and a minute later, the angle changes, the dorsal section is again seen getting bigger, and the ship disappears.
Continuity mistake: At the end, Picard is looking out the window when Worf comes in. There is a plant next to Picard in the close up, but it's missing in the long shots.
Continuity mistake: Picard states that the energy beam appears to come from the deflector array, in later shots it is coming from the rear of the star drive section.
Continuity mistake: Near the end of the episode, right after Lore fires the phaser at Dr. Crusher, Data tackles Lore and knocks the phaser out of Lore's hand. The phaser flies towards the cargo transporter and when it impacts, it breaks in two. You can see a piece of it go flying off to the left. Then shortly after when Data throws Lore onto the transporter pad and Lore picks up the phaser, it's in one piece again.
Continuity mistake: In the opening sequence, the venetian blinds in Dixon Hill's office rearrange themselves between takes. They're intact after the shooting, but moments later, despite being untouched by anyone in the room, they're broken and have a huge gap in them. (00:07:00)
Continuity mistake: In Ten Forward, when Deanna and Data are done playing 'chess', the positions of The Game-pieces on the lower board level between them changes repeatedly, depending on camera angle.
Continuity mistake: Just before Riker jumps through the portal with the female crew member he rescues, his phaser falls out of its holster, yet when he lands back in cargo bay 4 his phaser is right there in the holster.
Continuity mistake: On his way to the Farewell party, Picard is seen wearing his dress uniform, but no pips on it. There should be four.
Continuity mistake: Wesley says that he's departing shuttle bay 2, but on the floor, it says shuttle bay 3.
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