Revealing mistake: In the scene where Barclay reappears on the transporter with the crewmember, they both fall to the ground. The transporter chief had put up a forcefield around the transporter chamber, in case something goes wrong. However, when the crewmember falls to the ground, his foot goes right through where the forcefield is meant to be. It is still active, as only a few seconds later we see it being deactivated.
Continuity mistake: Data's insignia pips are backwards in the first scene as he is talking to Picard on the bridge.
Continuity mistake: When Deanna is trying to seduce Riker, she scratches him and there are three deep scratches on his neck. Later, when Doctor Crusher treats him, one of the scratches is now on his cheek, and only two are on his neck.
Other mistake: When Scotty goes to the holodeck to visit the original Enterprise, the computer tells him there are 5 Federation vessels with that name. (NX-01 served before the founding of the Federation so this is technically correct.) Scotty specifies NCC-1701, "no A, B, C or D." The computer then tells him the program is ready. The computer should have asked him if he wanted pre or post refit NCC-1701. The ship we see in the Original Series was rebuilt/refit into the ship we see in The Motion Picture.
Visible crew/equipment: In the scene where Geordi and the Captain are in engineering trying to close the subspace hole, you can see a silhouette of the camera in the reflection of the warp core blue lights in the window between the warp core and the console they are working from.
Visible crew/equipment: In the scene where Picard comes to engineering to ask Laforge if he has been successful in locating Riker's homing beacon, you can see the blue light of the warp core reflected in the window. Outlined in that reflection, near Geordi's chest, you can see a studio spotlight.
Continuity mistake: Just before Riker jumps through the portal with the female crew member he rescues, his phaser falls out of its holster, yet when he lands back in cargo bay 4 his phaser is right there in the holster.
Revealing mistake: In Amanda's quarters, when she repulses Q, as he flies toward the corner, you can tell it is his stunt double.
Revealing mistake: In the cargo bay, as Riker stands alone, through the whole scene where a case is about to hit him, you can tell it's a stuntman with a bad wig.
Continuity mistake: As Geordi talks to Ms. Rogers, Riker is walking in the background by some containers and a crewman in blue. After a cut to Ms. Rogers, Riker is suddenly alone with a data pad.
Continuity mistake: When young Picard sees his "father" Riker, he says to turn on the computer in schoolroom 8. In the scene showing the children gaining access to the computer, the terminal they are at shows classroom 7 across the header of the screen. (00:36:20 - 00:39:55)
Revealing mistake: When the first villain hits Worf with the chair, just as Alexander is yelling "look out", you can tell it is a stunt double.
Other mistake: In the transporter room, Data asks the computer what file log is shown. The computer reply is "Transport Log 759", Data confirms "That is the correct log", but the screen reads "Transport Log 721".
Plot hole: About two thirds of the way through this episode, Data deduces how Moriarty was able to 'leave' the holodeck. The big reveal is that he never did leave the holodeck, he merely reprogrammed it to simulate the rest of the ship without Picard, Barclay or Data's knowledge. While it is believable that this would fool humans like Picard and Barclay, it is ludicrous to suggest that Data would be taken in by it, even for a second. Data is an android whose perceptions of sight, sound and the world around him are far more sophisticated than humans. To list what we know of Data's perceptive abilities from previous episodes would take up the entire page, but suffice it to say he should have immediately recognised the 'Enterprise' as force fields and holograms rather than the genuine article. Note: this goes beyond a 'character mistake' or anything like that. Data's enthusiasm for Sherlock Holmes style deduction should have led him to eliminate the impossible before considering what was probable. Data accepts the impossibility of a holodeck character existing is the real world before discounting the possibility that it was still a holodeck simulation. This contradicts an awful lot of what is known about Data's abilities and powers of deduction. Although it serves for a good mystery the fact is it takes Data far longer than it should to deduce, or even guess at, the truth of their situation.
Other mistake: As the cloaked Warbird looks at the Enterprise, the registry number on the under side of the saucer is reversed.
Visible crew/equipment: During Data's second dream experience he imagines becoming a bird and flies through the Enterprise and beyond. As he flies past his father Soong standing at the anvil, a crew member is sitting on the floor by the double doors behind him. This has been edited out in some versions. (00:36:10)
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.
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.