Continuity mistake: As Q approaches Picard and Riker's position while playing a trumpet, both of Q's hands are on the horn. A second later, his left hand is down by his side. Then, after he makes cigars appear in Picard and Riker's mouths, his left hand is extended as he says the first part of his lines. A second later, both hands are on his horn.
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)