Visible crew/equipment: When Picard is in his quarters and Nella Daren stops by, you can see the boom mic at the top of the screen toward the left side. (00:11:30)
Revealing mistake: When Picard and Cmdr. Daron are in Picard's quarters together for the first time, watch Picard play his Inner Light theme. The hands playing the flute are obviously not his.
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