The Arsenal of Freedom - S1-E21
Continuity mistake: As the Enterprise is attacked, the registry number is reversed.
Visible crew/equipment: After Picard, Troi, and Worf have beamed down to the planet to meet Riva, when Harmony asks if they need food or refreshments, just as Picards says, "Thank you, no," a crewmember's elbow can be seen at the left side of the screen (this one is not visible on the Netflix version). Then when Troi says, "Your method of communication is elegant and quite beautiful," a crewmember (likely the same one as earlier) can be seen at the left side of the screen. (00:07:20 - 00:10:40)
Continuity mistake: When Data bends the bar, he does so much that the sides are almost parallel with a very acute angle. When Riker puts it on the desk, it's much more curved and the sides aren't as parallel anymore.
Continuity mistake: Data's insignia pips are backwards in the first scene as he is talking to Picard on the bridge.
When The Bough Breaks - S1-E17
Visible crew/equipment: When Data and Geordi come up to address Picard, there are two lines of tape on the floor for positions.
Visible crew/equipment: As Picard goes to sit in his seat, there's a shadow of the boom mike playing across the wall above Burke and Kolrami's heads.
Continuity mistake: In the opening sequence, the ship is positioned so that Shuttle Bay Two is aimed at the phenomena. But a moment later, the ship is facing into the stellar material.
Other mistake: As Guinan sits at the desk, she reaches toward, but doesn't touch, the control for the screen, but it activates.
Continuity mistake: As the ship fires the torpedoes, the familiar registry number on the underside of the saucer is completely missing.
Continuity mistake: Near the end of the episode, as they are preparing to beam down to the planet, Riker tells Warf to set his phaser on stun. He then holsters his own phaser and the transporter is activated. However, when they materialize on the planet, Riker is holding his phaser in his left hand.
Bloodlines - S7-E22
Visible crew/equipment: When Picard and his Jason have their "father and son" chat in the caves, you can see the mike shadow moving up and down a few times on Jason's leg. (00:33:20)
Yesterday's Enterprise - S3-E15
Other mistake: The Klingons ordering the Enterprise to prepare for boarding parties doesn't make sense. La Forge had announced only moments earlier that the Enterprise was on the verge of a warp core breach. The Klingons' ship's sensors should have been able to detect the Enterprise's impending destruction.
Conspiracy - S1-E25
Other mistake: When Riker is knocked into the glass table, he should have been bleeding from the impact, but when the close up shows him unconscious, he is not.
Revealing mistake: When the first villain hits Worf with the chair, just as Alexander is yelling "look out", you can tell it is a stunt double.
Encounter at Farpoint (1) - S1-E1
Other mistake: As the Enterprise starts to turn to starboard (right) to escape the energy field Q set up, as the field is moving to port (left, indicating the ship is turning right) the starfield is also moving right, when it should be moving left.
The Battle - S1-E9
Other mistake: When Capt. Picard gets beamed from The Stargazer back to The Enterprise at the end of the episode, he doesn't lower shields. Also, a Ferengi (DaiMan Bok) beams off the Stargazer onto his Ferengi ship earlier without lowering shields on the Stargazer. (00:35:45 - 00:44:20)
Continuity mistake: In the Engine Room, after Geordi calls Wesley and Data, Wes turns around and drops his hands. In the next shot, his hands are back up in front of him.
Suggested correction: Which episode is this for?