Encounter at Farpoint (1) - S1-E1
Revealing mistake: When Q freezes Torres on the bridge, it is easy to tell that directional hoses were used for the effect. (00:06:25)
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 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: 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.
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)
Conspiracy - S1-E25
Revealing mistake: As Riker swings on Quinn, and a moment later, tossed onto a glass table, both times it can be seen that it's Riker's stunt double.
Revealing mistake: When Data sits in his post, his neck pips are black and then gold. In the next jump scene when he is in the back of the bridge with his commanders, the pips are reversed.
Revealing mistake: As Riker is being dragged toward Armus, the wire pulling him can be seen disturbing the sand and the surface of the slime pool.
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 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.
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.
Revealing mistake: The 'dead' woman moves the barrel towards herself. (00:13:40)
Revealing mistake: In the corridor, as Wesley faces the Zaldan, the hallway behind the scene is obviously a painting due to the shadow of the support on the edges.
Who Watches The Watchers - S3-E4
Revealing mistake: About 38 minutes into the show, when Dr. Mary Warren dies and there's a close up of Picard & Nuria, you can see the her hand moving up and down as she breathes.
Conspiracy - S1-E25
Revealing mistake: After the fight with Riker, Quinn throws Worf through the room, hitting a wall. The replicator part of the wall moves.
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.