Encounter at Farpoint (1) - S1-E1
Continuity mistake: While trying to escape Q, the Enterprise fires eight torpedoes, but only five explode. If all detonated, the last three weren't shown, but Tasha reported detonation after only five. (00:15:30 - 00:17:10)
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)
Encounter at Farpoint (1) - S1-E1
Continuity mistake: The court announcer and the bell ringer bow respectively, and Q starts to depart. From Q's point of view, they start to bow again. (00:29:55)
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)
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 (2) - S1-E2
Continuity mistake: When Picard tells Q in the final scene "Get off my ship." Q is standing to his right, and Picard has his head turned towards Q. But when the angle changes to show Q's response, Picard is standing facing Q directly, and without his head turned.
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.
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: When Geordi is put onto a bed in sickbay there are two pillows - when he gets up to leave a little later they have disappeared.
Continuity mistake: At the very beginning of the Episode, Picard makes a log entry stating that the Enterprise is heading for the USS Tsiolkovsky at warp seven. Subsequent outside shots of the ship show it is traveling at impulse.
Continuity mistake: When Data brings up a picture of the original Kirk-era Enterprise in conjunction with the log talking about the water-intoxicant, the picture is of the refitted movie-style Enterprise - not the original round-nacelled model that was involved in the events of "The Naked Time."
Continuity mistake: While Troi and Yar are talking while holding hands in Troi's quarters, there is a piece of cloth between their hands in one camera angle, but in another camera angle, there is nothing between their hands.
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 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.
Where No One Has Gone Before - S1-E6
Continuity mistake: Picard addresses the ballerina as ensign, when in fact she has no pips on her uniform, making her a crewman.
Continuity mistake: When the two holographic villains are disintegrating outside the holodeck, there is a corridor opposite the holodeck. When the good guys exit a minute later, there is suddenly a solid wall. (00:38:20 - 00:39:20)
Continuity mistake: The lipstick on Picard changes between when he is kissed, and later when he leaves the holodeck (it's darker and on and above his lips.) Also, and more importantly, being holodeck matter, it should have disappeared after re-emerging in the real world.
Continuity mistake: After entering the Holodeck for the 2nd time, a vendor hands a folded piece of paper to Picard, yet Picard receives it unfolded.
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: After drinking some spiked Champagne from Lore, Data falls backward, yet lands on his face.
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.