The Best of Both Worlds (1) - S3-E26
Revealing mistake: During the phaser battle on the Borg ship, a detonation wire is seen attached to the right foot of the drone that Beverly kills.
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.
Data's Day - S4-E11
Revealing mistake: When Data asks the replicator for Feline supplement 74 and gives then gives it to Spot, a bug is crawling on the food. Replicators cannot create living organisms. (00:13:15)
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.
Revealing mistake: In an overhead shot of the Brattain, it's clear that the ship's (misspelled) name is just a poorly applied decal.
Revealing mistake: The Klingon which challenges Gowron, and which Gowron kills, is seen breathing when he should be stone dead. (00:16:10)
Revealing mistake: When Picard takes his seat in the Captain's chair after informing Dathon's crew he has been killed, the reflection of an overhead rig of gelled lights can be seen in the blade of Dathon's knife, which Picard is holding, as Picard says the line, "but at least they're not new enemies."
Revealing mistake: In season 5, "The Game," the brainwashed crew members hold Wesley's eyes open to force him to see the mind-controlling game. Their intention is to prevent him from closing his eyes, which would protect him from the device. While they are doing this, he blinks.
Revealing mistake: At the end of the episode, when Mrs. Troi enters Ten Forward naked, the flesh-colored top Majel Barrett is wearing is visible.
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.
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.
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.
Revealing mistake: When Picard and Cmdr. Daron are in Picard's quarters together for the first time, watch Picard play his Inner Light theme. The hands playing the flute are obviously not his.
Descent (1) - S6-E26
Revealing mistake: In the hand-to-hand with the Borg soldier, Data's stunt double is easily identifiable.
Revealing mistake: In the shot where Geordie walks into the bridge of his mother's ship and finds that everyone is dead, if you look closely at the bottom right of the screen as Geordie is walking into the bridge you can see that one of the containers on the ground is quickly moved into place by a woman who is dead. (00:13:40)
Revealing mistake: The 'dead' woman moves the barrel towards herself. (00:13:40)
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.