Continuity mistake: When checking Ian's pulse, Pulaski reaches out with her left hand, but her right arm retracts after the angle change.
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.
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.
Where Silence Has Lease - S2-E2
Continuity mistake: When Riker and Worf are beamed off the Yomato, Riker is on the left of Worf. When they materialize, Riker is on Worf's right.
Revealing mistake: As Data cautions La Forge not to say anything, his actual flesh tone is visible on his palm.
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.
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)
Other mistake: When Data is interpreting between Captain Picard and Riva, he uses signs for words Captain Picard has not yet spoken, and voices concepts before Riva has signed them. He also doesn't interpret everything the Captain and counselor Troi say.
Audio problem: After the offer of refreshments has been declined, Harmony says "I have been expecting you", but her mouth doesn't move.
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.
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: Looking at the shuttlecraft while sitting in the shuttle bay and after it has departed the Enterprise, you can tell they are different types of shuttles. The one in the shuttle bay has more angular lines with straight edges. The one outside the Enterprise has more curves than angles to its lines.
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.]
Visible crew/equipment: Data tells Maddox that he formally refuses to undergo the procedure, but he supports Maddox's intriguing ongoing work. After Maddox comments that Data is remarkable, Louvois takes note that Maddox referred to Data as "he" instead of "it," and when Louvois walks toward Picard the blue tape mark is visible on the floor where she stands. (00:43:00)
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.
Other mistake: After Riker turns off Data, Data slumps forward. After being in that position, and after the cut scene, Data's head twitches slightly.
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.
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.