The Best of Both Worlds (2) - S4-E1
Factual error: Shelby announces the Borg have entered Sector 001, and we get an exterior shot of the Borg ship flying past Saturn. The problem is that the Borg are approaching from the side of the planet illuminated by the sun, meaning they would actually be moving AWAY from Earth rather than toward it.
Remember Me - S4-E5
Visible crew/equipment: When Dr. Crusher is on the Bridge all alone, right before the "universe" collapses, the boom mic is reflected in the Red Alert rectangle next to the turbolift.
Revealing mistake: When the force field is activated in the Jeffries Tube, we only see the flash of light from off-screen. The effects team neglected to add the force field effect.
Half a Life - S4-E22
Visible crew/equipment: When Lwaxana and Deanna Troi are talking in Lwaxana's quarters (near the end of the episode), note the boom microphone you can see in the mirror as Lwaxana walks away from it the first time. Shadows from the boom microphone are also seen above Lwaxana's head on the wall. (00:40:20)
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".
Visible crew/equipment: When Riker approaches his "son" in the prison cell (right after he has discovered the first bluff) you can see the shadow of the mic boom on the back wall quickly moving from the middle to the right. (00:34:40)
Remember Me - S4-E5
Plot hole: When the image of the warp bubble closing in on the superimposed "Enterprise" image, Dr. Crusher asked for it to be the same scale for each image. At the rate the bubble was closing in on the engineering section, it would have been destroyed LONG before the 4 minutes 15 seconds the computer gave for it to be destroyed.
Other mistake: As Picard and Robert walk alongside the large bush just before their scuffle, two outgrowth branches on the bush get snagged onto the camera and can be seen snapping back into place.
Character mistake: Captain Picard wonders why the boy would want to go back to his captors if they abuse him and Dr. Crusher tells him it's not uncommon, it's called the Stockholm Syndrome as if Picard doesn't know or understand. However, in S03E12, "The High Ground", Dr. Crusher is held captive and when Picard is talking to her (after he is captured trying to rescue her), she begins to appear sympathetic to her captors and Picard says "I don't have to remind you of the psychological impact of being a hostage." Picard would be aware of why the boy may wish to return.
Devil's Due - S4-E13
Continuity mistake: As the camera does a close up on the shuttle craft's forward window as it approaches the Enterprise, the dorsal section is seen getting larger the closer they get. As Data and Picard talk, the image fades out, and a minute later, the angle changes, the dorsal section is again seen getting bigger, and the ship disappears.
Continuity mistake: At the end, Picard is looking out the window when Worf comes in. There is a plant next to Picard in the close up, but it's missing in the long shots.
Continuity mistake: In the opening sequence, the venetian blinds in Dixon Hill's office rearrange themselves between takes. They're intact after the shooting, but moments later, despite being untouched by anyone in the room, they're broken and have a huge gap in them. (00:07:00)
Continuity mistake: When commander Data is reciting the code to lock the rest of the crew out of the computer, he states the code '1-7-3-4-6-7-3-2-1-4-7-6-C-3-2-7-8-9-7-7-7-6-4-3-T-7-3-2-V-7-3-1-1-7-8-8-8-7-3-2-4-7-6-7-8-9-7-6-4-3-7-6-LOCK', but when the computer screen is shown the code reads '1-7-3-4-6-7-2-1-4-7-6-C-3-2-7-8-9-7-7-7-6-3-T-7-3-2-V-7-3-1-1-7-1-8-8-8-7-3-2-4-7-6-7-8-9-7-6-4-3-7-6-LOCK.'
Other mistake: The ship warp core was damaged by an explosion earlier and was offline in the first 32 minutes of the episode. But the ship's CGI indicates that it was online all through the episode.
Data's Day - S4-E11
Continuity mistake: At the end, Picard shows Data a baby born during the crisis. Neither of them touches it, but between shots, the baby's blanket changes positions. First it's almost completely covering his head and face, then it's pulled down and showing much more of him. (00:42:15)
Revealing mistake: In an overhead shot of the Brattain, it's clear that the ship's (misspelled) name is just a poorly applied decal.
Other mistake: As the camera looks at the Enterprise as a transitional view, part of the decal for the registry number is visible.
Data's Day - S4-E11
Revealing mistake: When Data and Dr. Crusher are tap dancing on the holodeck, whenever the camera angle changes to a wide shot from above (for the more complex dance moves), it's clear it is not Brent Spiner but a stand-in dancing.
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.