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."
Continuity mistake: After drinking some spiked Champagne from Lore, Data falls backward, yet lands on his face.
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: 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: 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.
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.
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: 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: 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: Several episodes have stardates after this episode, but still have Tasha Yar in them (even though she dies in this episode). They aired before this episode. The series producers later formalized their stardate system so that they take place in the order the episodes air.
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)
Continuity mistake: When the away team encounters the evil oily blob thing, it makes their equipment fly away. Later they have apparently recovered it. But strange things keep happening to Geordi's weapon: when he and the others run forward to rescue Riker, Geordi accidentally drops it in the black pool when he stops abruptly. Admittedly, you can't prove that's a mistake even though it has no purpose in the story. But shortly afterwards the phaser is back on Geordi's belt, clean. Did the sticky, malicious, bullying blob give it back just like that? (People often try and find justifications for mistakes, but in this case, wishful thinking can only give us an extremely unlikely explanation.)
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: Watch when Geordi on the bridge calls up Dr. Crusher in Sick Bay. There's a white-haired medical assistant working on someone behind Geordi. Then when Dr. Crusher responds to Geordi's page, the same assistant is down in Sick Bay with her. Then they cut back to Geordi and the assistant is back up on the bridge again.
When The Bough Breaks - S1-E17
Continuity mistake: When Wesley is being introduced to the Companion, the camera zooms in to see the entire console up on the full screen with NO hands on it, but when it cuts to a side view, Radue's wife's hands are on the console.
Continuity mistake: When Beata tells Riker that he attracts her like no other man, her hand disappears from his neck.
Conspiracy - S1-E25
Continuity mistake: As the ship enters Sector 63, there's a shot of the Conn and Ops positions and the screen. Geordi is in the right chair, the left is empty. Data is nowhere on the bridge, but when as Picard walks forward, Data's arm is suddenly in position.
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)
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.