Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
Revealing mistake: When Data sits in his post, his neck pips are black and then gold. In the next jump scene when he is in the back of the bridge with his commanders, the pips are reversed.
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."
Revealing mistake: When Picard looks out the window of the Dixon Hill office he sees the cars passing by each other, the traffic light is right in front of the window as if the entire building is not only in the middle of the street but only one story high.
Revealing mistake: In the corridor, as Wesley faces the Zaldan, the hallway behind the scene is obviously a painting due to the shadow of the support on the edges.
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.
Revealing mistake: As Riker is being dragged toward Armus, the wire pulling him can be seen disturbing the sand and the surface of the slime pool.
Conspiracy - S1-E25
Revealing mistake: As Riker swings on Quinn, and a moment later, tossed onto a glass table, both times it can be seen that it's Riker's stunt double.
Conspiracy - S1-E25
Revealing mistake: After the fight with Riker, Quinn throws Worf through the room, hitting a wall. The replicator part of the wall moves.
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.
Where Silence Has Lease - S2-E2
Revealing mistake: When the black deck officer is supposed to be dead you can see the actor's nostrils flaring as he is breathing.
Revealing mistake: As Data cautions La Forge not to say anything, his actual flesh tone is visible on his palm.
Revealing mistake: When looking at Kolrami, the line between his make up and actual skin tone can be seen between his scalp, hairline, and the back of his neck.
Who Watches The Watchers - S3-E4
Revealing mistake: About 38 minutes into the show, when Dr. Mary Warren dies and there's a close up of Picard & Nuria, you can see the her hand moving up and down as she breathes.
Yesterday's Enterprise - S3-E15
Revealing mistake: When Tasha and Castillo walk up to the bar in Ten Forward, Whoopi Goldberg can be seen standing outside the door waiting for her cue to walk in the room.
Revealing mistake: Just after Riker and Geordi are talking in the turbo lift, it cuts to a view from outside the ship and shows the USS Hood flying next to the USS Enterprise. As the ships draw nearer, the views of both ships overlap, and a black mat outline can be seen around the saucer section of the Hood as it passes by the Enterprise's starboard nacelle.
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.