Revealing mistake: At the end of the episode, when Mrs. Troi enters Ten Forward naked, the flesh-colored top Majel Barrett is wearing is visible.
Other mistake: While down in the pit Geordi makes a couple of spikes to climb out with. When the phaser beam is melting the ore, the metal goes molten about two inches in front of the beam. Also, the spikes are rounded, like handles. The molds he made would have left a flat side.
Other mistake: One of the physical appearances Lal considers adopting is an Andorian female with green skin. In the Trek universe, Andorians invariably have blue skin (the Aenar are a variant of the Andorian race but are depicted with bluish-white skin, still not green). And while other humanoid races have been portrayed with different skin tones, there are some races that have only one skin hue. (ie, Andorians are always blue, Orions are always green, Ferengi are always light orange.) It is highly unlikely she or Data designed it with different skin as Data wants her to fit in, and Troi makes no mention of it.
Revealing mistake: When Picard looks out the window of the Dixon Hill office he sees the cars passing by each other, the traffic light is right in front of the window as if the entire building is not only in the middle of the street but only one story high.
Visible crew/equipment: When Worf addresses Klingon captain K'Nera, a microphone dips into the shot over Worf's head. (00:33:10)
Visible crew/equipment: In the scene in the cavern where Wesley fires his phaser to heat the rocks to keep him and Picard warm, Wesley's shadow is in the wrong place. The camera is in almost a direct line of sight between where the rocks are (which are supposed to be providing the light source) and Wesley with the cavern wall behind him. After Wesley fires his phaser and the room illuminates, his shadow should be either directly behind him or to the left of him, but his shadow appears to the right side of him. The only way his shadow would be there was if the light source was off camera a good distance to the left.
Conspiracy - S1-E25
Other mistake: When Riker is knocked into the glass table, he should have been bleeding from the impact, but when the close up shows him unconscious, he is not.
Nth Degree - S4-E19
Other mistake: After Data reports the bypass blocked, Riker goes to call to Barclay. The chirp preceding the computer, now Barclay's, response occurs almost simultaneously with the call, rather than a second or two gap between the call and chirp.
Where Silence Has Lease - S2-E2
Continuity mistake: When Riker and Worf are beamed off the Yomato, Riker is on the left of Worf. When they materialize, Riker is on Worf's right.
Revealing mistake: The Klingon which challenges Gowron, and which Gowron kills, is seen breathing when he should be stone dead. (00:16:10)
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