The Royale - S2-E12
Continuity mistake: When Data is first playing Blackjack, his first face up card dealt is a 7, followed by a 5. In the close up when the final card is dealt, the first two cards are now 3 and 2.
Continuity mistake: When Data is telling Guinan jokes and is then called to the bridge, he's holding the cigar between his first two fingers. In the next shot, he's holding the cigar between his thumb and first finger.
The Dauphin - S2-E10
Continuity mistake: When Wesley and Salia are on the holodeck looking at Roseau 5, Salia's left arm is around Wesley's back. In the next shot, both her hands are wrapped around his arm.
Continuity mistake: Near the end, when Pulaski finally stops the infection in Riker and is just about to contact Picard with her success, look at Riker lying on the table. His eyes are open, then he closes them slowly. The next scene has Riker opening his eyes for the first time after recovering from the procedure.
Other mistake: In this episode, in Riker's memory, the encounter between him and Quinn is re-lived. As Quinn starts to attack Riker, you can see Riker's stunt double's face, and tell that it's Quinn's stunt double, as the hair is smooth, not styled. Also, Riker is a few inches taller than Quinn, but in the onset of the attack, they're equal heights.
Continuity mistake: After Pulaski examines Riker's leg, and readies to beam up, he leans to the right to get up. In the wide shot, he does it again.
Revealing mistake: As Data cautions La Forge not to say anything, his actual flesh tone is visible on his palm.
Visible crew/equipment: After Picard, Troi, and Worf have beamed down to the planet to meet Riva, when Harmony asks if they need food or refreshments, just as Picards says, "Thank you, no," a crewmember's elbow can be seen at the left side of the screen (this one is not visible on the Netflix version). Then when Troi says, "Your method of communication is elegant and quite beautiful," a crewmember (likely the same one as earlier) can be seen at the left side of the screen. (00:07:20 - 00:10:40)
Continuity mistake: When Data bends the bar, he does so much that the sides are almost parallel with a very acute angle. When Riker puts it on the desk, it's much more curved and the sides aren't as parallel anymore.
Visible crew/equipment: As Picard goes to sit in his seat, there's a shadow of the boom mike playing across the wall above Burke and Kolrami's heads.
Other mistake: As Guinan sits at the desk, she reaches toward, but doesn't touch, the control for the screen, but it activates.
Continuity mistake: As the ship fires the torpedoes, the familiar registry number on the underside of the saucer is completely missing.
Continuity mistake: Near the end of the episode, as they are preparing to beam down to the planet, Riker tells Warf to set his phaser on stun. He then holsters his own phaser and the transporter is activated. However, when they materialize on the planet, Riker is holding his phaser in his left hand.
Visible crew/equipment: In the Medical center, as the camera pulls back from Picard, who is lying on the bio bed, the camera is reflected on the panels angled toward the camera.
Audio problem: We hear Reva's female member of his choir say "I have been expecting you", but her mouth doesn't move.
Continuity mistake: As Worf goes to enter the portal to the Enterprise carrying Data, his right hand is free, and his left is holding Data's left hand. Appearing on the bridge, Worf's left hand is on Data's leg, his right hand on Data's wrist.
Where Silence Has Lease - S2-E2
Visible crew/equipment: As Picard approaches Data's position, the boom mike is reflected on the panel behind him.
Visible crew/equipment: As Kolrami talks to Picard from beside the aquarium, you can see the studio light panels reflected on the glass.
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.