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).
Visible crew/equipment: During the scan of the temporal rift at the beginning of the episode, the tip of the microphone briefly comes into view at the top of the screen above Captain Picard's head when Data says, "Nothing I have seen before." [Not visible in the remastered Blu-ray version].
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: When Data goes into his laughing fit, Troi is at her regular seat, but when he stops and remarks it was a wonderful feeling, the wide shot of the crew shows her seat empty. But then, when Picard is hailed, when the moon returns to its orbit, Troi is back at her seat.
Other mistake: During his final discussion with Tomalok, Picard tells him that the Enterprise will escort the Romulan ship back to The Neutral Zone. However, as the episode ends, the two ships are heading off in opposite directions. Both the Enterprise and Romulan warbirds have demonstrated in the past that they can spin on their axis from a standstill. There is no reason for either ship to head away from the other to turn around.
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.