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.
Continuity mistake: When Wesley Crusher and his school chum accidentally hit Picard with a snowball from the holodeck doorway, it makes a huge wet spot on the captain's left shoulder. However, when Picard tells them "Don't let it happen again," as he turns to walk away, the wet spot is now suddenly dry. (00:36:00)
Plot hole: The entire premise of the episode is contradictory; the franchise makes abundantly clear through the so called Prime Directive that the Federation abides to a code (often creating moral dilemmas that may require to stretch the rules) that says that their staff is not supposed to interfere in world that haven't reached warp capabilities, nor involve themselves in their internal matters. In the first half of the episode, Riker and the others just go 'mingle' with the frisky natives without a care in the world, and yet in the second half the Prime Directive itself is referenced explicitly and it is part of the plot.
Continuity mistake: After Geordi separates the ship, the saucer was well away from the star drive section, and they're at impulse power. When the star drive section goes to turn around, it is at warp speed, and it is a re-use of the high warp separation sequence from Episode One "Encounter at Farpoint."