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)
Visible crew/equipment: In the scene where the Enterprise encounters the Ferengi transport ship, the boom microphone is visible behind Commander Riker just as Data sits down at the controls.
Continuity mistake: In the very first scene when Data stands up to explain the situation to the Senior Staff, you can see that Lt. Worf has his elbow off the table and Dr. Crusher has her arms uncrossed. In the next shot the camera cuts in front of them and Lt. Worf has his elbow on the table while Dr. Crusher's hands are crossed even though Data is still on the same sentence.
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