Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
The Royale - S2-E12
Factual error: 30 seconds in Geordi says: 'surface temperature -291 degrees Celsius'. (The scale only goes down to -273.15 which is absolute zero). (00:00:30)
The Best of Both Worlds (2) - S4-E1
Factual error: Shelby announces the Borg have entered Sector 001, and we get an exterior shot of the Borg ship flying past Saturn. The problem is that the Borg are approaching from the side of the planet illuminated by the sun, meaning they would actually be moving AWAY from Earth rather than toward it.
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. (00:21:45)
Conspiracy - S1-E25
Continuity mistake: In the beginning of this episode, Riker orders Geordi (who was navigator at the time) to increase to Warp 6. In response, Geordi replies, "Aye sir, full impulse."
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)
Revealing mistake: In Amanda's quarters, when she repulses Q, as he flies toward the corner, you can tell it is his stunt double.
Remember Me - S4-E5
Visible crew/equipment: When Dr. Crusher is on the Bridge all alone, right before the "universe" collapses, the boom mic is reflected in the Red Alert rectangle next to the turbolift.
Visible crew/equipment: When Picard, Spock, and Data have just escaped from Romulan Commander Sela, when they are walking out of the room look at the green glass ornament - you can see a reflection of a crew member. Corrected on Blu-ray. (00:41:10)
Revealing mistake: In the scene where Barclay reappears on the transporter with the crewmember, they both fall to the ground. The transporter chief had put up a forcefield around the transporter chamber, in case something goes wrong. However, when the crewmember falls to the ground, his foot goes right through where the forcefield is meant to be. It is still active, as only a few seconds later we see it being deactivated.
Visible crew/equipment: When Riker goes to meet Beata, they sit on the bed together drinking something. As Beata puts her glass down, a hand in the lower right-hand corner reaches for it and removes it for her.
Continuity mistake: When Dr Marr and Data are talking in the cave about her dead son, she is holding the tricorder upside down.
Yesterday's Enterprise - S3-E15
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 drinking some spiked Champagne from Lore, Data falls backward, yet lands on his face.
Visible crew/equipment: When Riker tells Yar to open a channel to the Jarada, you can see the reflection of a boom mic in the workstation along the back wall behind him.
Revealing mistake: In season 5, "The Game," the brainwashed crew members hold Wesley's eyes open to force him to see the mind-controlling game. Their intention is to prevent him from closing his eyes, which would protect him from the device. While they are doing this, he blinks.
Continuity mistake: When Picard asks the Ferengi if they are withdrawing their surrender, Yar's arms pop back and forth from folded to extended as the shots change.
Answer: Yes. The doors to the holodecks can be locked when in use by anyone aboard the Enterprise so they couldn't be disturbed. However, high ranking officers like Captain Picard could override the doors as it's seen that overrides are in use even for the crews quarters. Even Barclay, when he's indulging in one of his fantasies could have the doors to the holodeck unlocked by an override code.