Continuity mistake: The creators re-did the titles from the third season on, but only from before the shot of the ringed planet, and they didn't make sure they matched. Compare the movement of the stars inside the rings and the star field outside the rings - they move in different directions compared to each other.
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)
Continuity mistake: Commander Data tells Picard the Saucer Section will arrive in 51 minutes. Riker's synopsis audio can be heard in the background without interruption, and shortly after Data says this, the cameras turn back to Riker and the Video synopsis ends. Riker immediately reports to Picard who then receives the message that the Saucer Section is in orbit. Now, Riker was watching highlights of video footage from the Bridge, of which we see almost all of it because there really wouldn't be that much to view. And that's really all he could watch since we don't have cameras in the "Q-verse" and we see the footage ending with the Q sphere chasing the ship. Also, the entire ordeal was far less than an hour so there's no way a highlight reel could take an hour, not to mention the uninterrupted audio. We seem to be missing almost an entire hour. (00:37:32)
Continuity mistake: When Picard tells Q in the final scene "Get off my ship." Q is standing to his right, and Picard has his head turned towards Q. But when the angle changes to show Q's response, Picard is standing facing Q directly, and without his head turned.
Continuity mistake: The computer is directing Commander Riker toward L.C. Data in holodeck area 4-J. As he walks along the corridor the computer helps him by saying that he should go to "the next hatchway on your right." Then Riker turns left (according to the way he was going) to enter the holodeck.
Continuity mistake: When Data brings up a picture of the original Kirk-era Enterprise in conjunction with the log talking about the water-intoxicant, the picture is of the refitted movie-style Enterprise - not the original round-nacelled model that was involved in the events of "The Naked Time."