Other mistake: At the beginning of the episode, when Picard and Riker leave the bridge to head to the teleport deck to receive the admiral and his wife, as the lift door opens Patrick Stewart makes a face at the film crew off-screen as he walks off the bridge. (00:02:05)
Other mistake: After greeting Crusher, Data explains where Picard is. Problem is he uses the contraction "he's" instead of "he is." Data is supposed to be incapable of this.
Suggested correction: This is only a mistake if the series is taken as a whole. At this point in the series, that particular trait wasn't part of the character. Data uses contractions multiple times in the first season, as the trait was added later.
While it was explicitly expressed in season 2 that Data can not use contractions, the fact that they did established this character trait means it's a valid mistake since the trait is meant to show Data could never use contractions since his creation, not that he suddenly developed it some 30-odd years later. Although it would probably be better to establish one character mistake for "all of season 1" than list every individual time it happened.
Encounter at Farpoint (1) - S1-E1
Other mistake: When Q the Judge enters on his throne, at one point, the hydraulic arm the throne is on is visible, despite being black to blend in. Conversely, in "All Good Things...", the final episode, the arm is missing having been matted out by CGI techniques.
Other mistake: In this episode, when Riker makes his log entry, he says the stardate is "4124.5, " the 4-digit style of stardates from The Original Series, rather than the 5 digit style used in The Next Generation.
Other mistake: As the ship approaches the energy cloud the second time, the registry number on the underside of the saucer is backwards.
Encounter at Farpoint (1) - S1-E1
Other mistake: As the Enterprise is fleeing from Q, it peaks around Warp 9.6 which according to the fact books, translates to around 1000c in sidereal space. Also according to the fact books, the saucer section is not capable of sustained Warp flight on its own. Also, at the beginning of The Chase scene, the Enterprise is on course to Farpoint, Q's fence is perpendicular to it. The Enterprise does at least a 90°+ turn beginning her escape maneuver prior to separation, so it is definitely not flying past Farpoint during The Chase. Still the saucer section somehow makes it to Farpoint a mere 51 minutes after the engine section. There's no evidence at all in the dialog that it was Q's doing.
Other mistake: As Crusher enters the police station, Data says "Hiya, Doc. What's cookin?" He's supposed to be incapable of using contractions.
Other mistake: As the Enterprise comes into the frame approaching the cloud, the registry numbers are reversed.
Where No One Has Gone Before - S1-E6
Other mistake: As the Enterprise comes out of warp in galaxy M33, the conference lounge is visible and is a re-use of the opening sequence. The movements of the people is identical.
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)
