Continuity mistake: In the scene where Picard is talking to the governor about staying awhile to fix the weather controls, Troi can be seen in the background talking to some people, but she had just left with Beverly to go to Nana's house.
Continuity mistake: After Wesley makes his neutrino pulse suggestion, Picard tells him to go do it. Wesley walks off camera. Then there's a commercial break, and Wesley is back on the bridge in the long shots. A few minutes later we hear the turbo-lift and Wesley walks back onto the bridge.
Continuity mistake: When Data and Troi are scanning the list of elements, searching for something to cause an explosion, the list is scrolling "up" the screen. When she tells Data to stop and go back, he does, but the list continues to scroll "up" instead of back "down".
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: In the very first scene when Data stands up to explain the situation to the Senior Staff, you can see that Lt. Worf has his elbow off the table and Dr. Crusher has her arms uncrossed. In the next shot the camera cuts in front of them and Lt. Worf has his elbow on the table while Dr. Crusher's hands are crossed even though Data is still on the same sentence.
Continuity mistake: The stardate given in the previous episode is 46578.4 and the stardate of the episode after this is 46682.4. In this episode, Picard records the stardate in his log as 46759.2. There was either a typo in the script or the actor misspoke the scripted 46579.2. This isn't excusable as a character error, because the episode is accepted in Trek lore as occurring on the date Picard states.
Continuity mistake: The Bringloidi leader keeps saying that they've spent 300 years building their society, but this episode takes place in 2365, and it's stated that his ship launched in 2123, making it 200 years.
Continuity mistake: When Ro and Picard are among Ro's people and she gives her jacket to a child (saying something like 'this is what I was, once') she never removes her commbadge. However, there's a commbadge neatly placed on her grey tank top - even though she didn't even remove it from the jacket, let alone put it on her shirt.
Continuity mistake: It is stated that the Traveller is from Tau Ceti, but in his previous two appearances he was from Tau Alpha C.
Continuity mistake: For some reason the back of the chairs in Picard's shuttlecraft have Romulan insignia on them.
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.
Continuity mistake: Klingons measure distance in kilometers in this episode. However, in all other Trek shows and movies, they measure in kellicams. [This was apparently during a misguided attempt by the Empire to adopt the decimal system (for Galactic consistency), even though the change was wildy unpopular with the public and military alike. While some ships, like in this episode, gave it a good try, the change was short-lived and eventually abandoned. However, until this claim can be backed up by a reference within Star Trek canon, it stands as a mistake.]
Bloodlines - S7-E22
Continuity mistake: When Jason and Picard are having a conversation in the holodeck, Jason says "I remember her telling me about all the boys and girls who didn't have anyone to care for them" while looking in the opposite direction of where Picard is sitting. The camera angle changes to a close-up and Jason now has his head turned slightly towards Picard.
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: In the scene where Captain Picard reaches for the aged fruit, he screams while holding his right wrist with his left hand. As Troi, Geordi, and Data rush in you can see Captain Picard holding his wrist up in the air. The camera then cuts directly in front of Captain Picard and you can see Troi scanning his wrist but he isn't holding his wrist anymore. The camera then cuts directly in front of Troi and Geordi and you can see that Captain Picard is still holding his wrist. The camera then again cuts back to Captain Picard and he isn't holding his wrist anymore.
Continuity mistake: When Beata tells Riker that he attracts her like no other man, her hand disappears from his neck.
Continuity mistake: Lwaxana and Deanna get in an elevator and Deanna tells it to go to Deck 8. But when they arrive the sign says 12 Turbolift.
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.