Visible crew/equipment: Boom action is visible in reflections on computer consoles in the back, while Picard and LaForge talk to each other on the bridge. (00:40:15 - 00:40:46)
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.
Continuity mistake: When Lore backhands Worf in the turbolift, his eyes close but open back up as he is sinking down. Then, in the close-up, his eyes are closed again.
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.
Conspiracy - S1-E25
Continuity mistake: Lt. Commander Remmick has three solid pips on his uniform when Admiral Quinn is beamed to the Enterprise, implying his rank to be Commander rather than Lt. Commander. In all other shots in the episode, his rank is displayed as Lt. Commander. (00:25:11)
Audio problem: After the offer of refreshments has been declined, Harmony says "I have been expecting you", but her mouth doesn't move.
Continuity mistake: Near the end, after being subjected to the snowy scene, only Mr. Leech has snowflakes on him. They're on him as he steps into the corridor, then they're suddenly gone.
Deliberate mistake: To fix the error of the Enterprise firing phasers from the torpedo bay, the Blu-ray version uses footage from "The Best of Both Worlds" to show phasers firing from the dorsal emitter. In doing so, they created a new goof; the planet El Adrel is not visible in the background during these shots.
Suggested correction: I rewatched the original version on the old DVDs. El Adrel wasn't visible in the original either, so this is not a new error.
Audio problem: Near the end, when Leech points his gun at Crusher, there is the sound of him cocking the weapon. However, when we see his gun immediately thereafter, the hammer is in the uncocked position.
Visible crew/equipment: In Wesley's quarters, when the camera looks at Geordi, there appears to either be a person reflected on Wesley's device or a boom mic shadow plays across it.
Continuity mistake: When Yar is transported back to the ship her weapon was on her left arm. When on the transporter pad the weapon is on her right arm.
Visible crew/equipment: When Dr. Crusher is trying to save the Borg, just before Worf says "lower the force field" a boom mic is visible.
Visible crew/equipment: Numerous times throughout the series, the screws that hold on the panel faces on the Conn and Ops positions are visible.
Other mistake: As the ship approaches the energy cloud the second time, the registry number on the underside of the saucer is backwards.
Gambit (2) - S7-E5
Other mistake: When the raiders' vessel fires on the Enterprise, only the starboard nacelle is hit. Right after the impact, Worf reports the port nacelle hit, then the starboard.
Other mistake: As the camera looks at the Enterprise as a transitional view, part of the decal for the registry number is visible.
Continuity mistake: In the opening scene, Riker's rank pips are diagonal on his collar. Then in Worf's quarters, the pips are level as they should be.
Character mistake: When Data and Picard discover Troi in her bathtub, Data scans her and comments that she is technically no longer "human." While Troi is indeed half human, she has the features of a Betazoid (black eyes and empathic abilities) and consistently describes herself and is described by others as a Betazoid. It is unusual for anyone to describe Troi as being "human", and it is unfathomable that Data would make that mistake.
