Encounter at Farpoint (1) - S1-E1
Continuity mistake: As Q comes into the courtroom on his floating dais, he goes to his right and gestures to the people to sit. He then starts to his left, and puts his hand down. After the angle cuts to Picard's point of view, as Q goes left his hand is dropping to the arm rest again. (00:21:35)
Continuity mistake: Near the end of the episode, right after Lore fires the phaser at Dr. Crusher, Data tackles Lore and knocks the phaser out of Lore's hand. The phaser flies towards the cargo transporter and when it impacts, it breaks in two. You can see a piece of it go flying off to the left. Then shortly after when Data throws Lore onto the transporter pad and Lore picks up the phaser, it's in one piece again.
Continuity mistake: On his way to the Farewell party, Picard is seen wearing his dress uniform, but no pips on it. There should be four.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: Commander Data tells Picard the Saucer Section will arrive in 51 minutes. Riker's synopsis audio can be heard in the background without interruption, and shortly after Data says this, the cameras turn back to Riker and the Video synopsis ends. Riker immediately reports to Picard who then receives the message that the Saucer Section is in orbit. Now, Riker was watching highlights of video footage from the Bridge, of which we see almost all of it because there really wouldn't be that much to view. And that's really all he could watch since we don't have cameras in the "Q-verse" and we see the footage ending with the Q sphere chasing the ship. Also, the entire ordeal was far less than an hour so there's no way a highlight reel could take an hour, not to mention the uninterrupted audio. We seem to be missing almost an entire hour. (00:37:32)
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.
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)
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.
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.
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.
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.
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 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."
Continuity mistake: As Lore opens a channel, there's a blinking red light over the key he uses that disappears after the angle change.
Encounter at Farpoint (2) - S1-E2
Continuity mistake: The "loose rock" Wesley falls from didn't move at all the way it did with Riker.
Continuity mistake: As Data, Geordi, and Will pause to consider a route around Engineering section, the smoky mist is chest high. After the angle change it's thinner and shin height.
Continuity mistake: On the freighter, when Geordi looks at Data, the image on the Bridge view screen has Data's hair in an unkempt, or unusual style. When the scene shifts back to the freighter, Data's hair is straight back.
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.