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.
Other mistake: As the ship approaches the energy cloud the second time, the registry number on the underside of the saucer is backwards.
Character mistake: When the away team transports down to the planet, Data is wearing three full rank pips denoting the rank of a full Commander, rather than his actual rank of Lieutenant Commander. (00:09:39)
Revealing mistake: In the sickbay, the wall where the biobeds are located can be easily seen as a wall used for what would be in the Conference lounge. The alcoves have a fabric covering the windows, and it appeared to be a hastily done redress.
Continuity mistake: When the technician goes to revive Claire, in the long shot, her eyes open. In the close up, she "comes to" again, opening her eyes.
Encounter at Farpoint (2) - S1-E2
Continuity mistake: The computer is directing Commander Riker toward L.C. Data in holodeck area 4-J. As he walks along the corridor the computer helps him by saying that he should go to "the next hatchway on your right." Then Riker turns left (according to the way he was going) to enter the holodeck.
Conspiracy - S1-E25
Continuity mistake: After leaving the table in headquarters, Picard meets Riker at the door. In the far shots, Picard has his back to the table. In the close up, his left shoulder is towards the table.
The Arsenal of Freedom - S1-E21
Continuity mistake: As the Enterprise is attacked, the registry number is reversed.
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.
Other mistake: As Crusher enters the police station, Data says "Hiya, Doc. What's cookin?" He's supposed to be incapable of using contractions.
Revealing mistake: As Data looks at the information on Dixon Hill, as the computer flash feeds, you can see that it's all the same block of information starting with the title of the first novel, which is the title of the episode, "The Big Goodbye."
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.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Riker looks at the wooded scene on the holodeck, the water is flat calm, but when the camera looks at him, the water is noticeably more agitated before he gets to the rocks.
Encounter at Farpoint (1) - S1-E1
Visible crew/equipment: As Zorn leans over his desk after Riker leaves, the studio light is reflected on the monitor screen to his left.
Continuity mistake: When Wesley Crusher and his school chum accidentally hit Picard with a snowball from the holodeck doorway, it makes a huge wet spot on the captain's left shoulder. However, when Picard tells them "Don't let it happen again," as he turns to walk away, the wet spot is now suddenly dry. (00:36:00)
We'll Always Have Paris - S1-E24
Continuity mistake: The red towel Picard holds goes from draped over the front of the arm rest, to over his hand between angles.
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)
The Arsenal of Freedom - S1-E21
Revealing mistake: As Data ducks to avoid the blast from the probe, the scene shifts to a wide shot. After Data tosses Yar to safety, he jumps after her. As he does, you can tell it's a stunt man with a bad wig.
The Arsenal of Freedom - S1-E21
Continuity mistake: After Geordi separates the ship, the saucer was well away from the star drive section, and they're at impulse power. When the star drive section goes to turn around, it is at warp speed, and it is a re-use of the high warp separation sequence from Episode One "Encounter at Farpoint."
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.