Continuity mistake: In the episode 'Yesterday's Enterprise' (season three, episode 15), watch the final scene with Geordi and Guinan in Ten-Forward. Although time and the universe has returned to normal, Geordi is still wearing the uniform from the alternate timeline (note the sleeve detail, and the extended neck piece).
Continuity mistake: After Wesley makes his neutrino pulse suggestion, Picard tells him to go do it. Wesley walks off camera. Then there's a commercial break, and Wesley is back on the bridge in the long shots. A few minutes later we hear the turbo-lift and Wesley walks back onto the bridge.
Continuity mistake: At the end of Barclay's sword fight on the holodeck, he has the hologram of captain Picard against a wall. When the angle is on the hologram, Barclay's sword is pressed into his chest. However, when the angle is on Barclay, the sword is several inches away from the hologram.
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: While Tam is talking to Deanna and sits down, he says "You understood... at least a little, how I felt." While saying this, he places his left hand on his right leg. While still saying that same line, it cuts to an angle from beside Deanna and his left hand is suddenly between his legs.
Continuity mistake: To view their orders and mission, Data puts a drive into the Enterprise's computer while standing with Riker and Geordi. Riker is seen standing but leaning casually away from Data on Data's right, and Geordi is standing off to Data's left. It then cuts show the computer screen, and the three men are reflected in it. The reflection shows that Riker is suddenly almost leaning over Data's shoulder, and Geordi has moved to standing behind Data's left shoulder.
Continuity mistake: In the beginning of the episode, right after Data informs Picard that the USS Hood is on an intercept course, closing at high warp, Picard is shown in the back ground looking down at his arm rest. He looks up and turns his head to his right making it center with his body. It then cuts to a close up of Picard and he is looking to his left, and turns his head again to say "That's odd."