Conspiracy - S1-E25
Continuity mistake: In the beginning of this episode, Riker orders Geordi (who was navigator at the time) to increase to Warp 6. In response, Geordi replies, "Aye sir, full impulse."
Continuity mistake: When Dr Marr and Data are talking in the cave about her dead son, she is holding the tricorder upside down.
Yesterday's Enterprise - S3-E15
Continuity mistake: In the episode 'Yesterday's Enterprise' (season three, episode 15), watch the final scene with Geordi and Guinan in Ten-Forward. Although time and the universe has returned to normal, Geordi is still wearing the uniform from the alternate timeline (note the sleeve detail, and the extended neck piece).
Continuity mistake: After drinking some spiked Champagne from Lore, Data falls backward, yet lands on his face.
Continuity mistake: When Picard asks the Ferengi if they are withdrawing their surrender, Yar's arms pop back and forth from folded to extended as the shots change.
Continuity mistake: In Ten Forward, when Deanna and Data are done playing 'chess', the positions of The Game-pieces on the lower board level between them changes repeatedly, depending on camera angle.
Where No One Has Gone Before - S1-E6
Continuity mistake: Picard addresses the ballerina as ensign, when in fact she has no pips on her uniform, making her a crewman.
Continuity mistake: The lipstick on Picard changes between when he is kissed, and later when he leaves the holodeck (it's darker and on and above his lips.) Also, and more importantly, being holodeck matter, it should have disappeared after re-emerging in the real world.
Continuity mistake: When Geordi is put onto a bed in sickbay there are two pillows - when he gets up to leave a little later they have disappeared.
Continuity mistake: At the very beginning of the Episode, Picard makes a log entry stating that the Enterprise is heading for the USS Tsiolkovsky at warp seven. Subsequent outside shots of the ship show it is traveling at impulse.
Encounter at Farpoint (2) - S1-E2
Continuity mistake: When Picard tells Q in the final scene "Get off my ship." Q is standing to his right, and Picard has his head turned towards Q. But when the angle changes to show Q's response, Picard is standing facing Q directly, and without his head turned.
Continuity mistake: When Data brings up a picture of the original Kirk-era Enterprise in conjunction with the log talking about the water-intoxicant, the picture is of the refitted movie-style Enterprise - not the original round-nacelled model that was involved in the events of "The Naked Time."
Continuity mistake: After entering the Holodeck for the 2nd time, a vendor hands a folded piece of paper to Picard, yet Picard receives it unfolded.
Continuity mistake: In the scene right before the shuttle's crew finds the Romulan ship and the Enterprise, Geordi calls the shuttle craft's cockpit to explain the temporal disturbances. Captain Picard, Troi and Data walk into the shuttle's cockpit room and Troi puts her right arm on Geordi's chair. As Geordi, Data and Captain Picard are talking you can see Troi's wrist hanging off the chair, but when the camera cuts directly in front of Geordi her whole wrist is on the chair. The camera then cuts back and you can see that Troi's wrist is still hanging off the chair.
Continuity mistake: The creators re-did the titles from the third season on, but only from before the shot of the ringed planet, and they didn't make sure they matched. Compare the movement of the stars inside the rings and the star field outside the rings - they move in different directions compared to each other.
Continuity mistake: While Troi and Yar are talking while holding hands in Troi's quarters, there is a piece of cloth between their hands in one camera angle, but in another camera angle, there is nothing between their hands.
Continuity mistake: Several episodes have stardates after this episode, but still have Tasha Yar in them (even though she dies in this episode). They aired before this episode. The series producers later formalized their stardate system so that they take place in the order the episodes air.
Continuity mistake: In the beginning of the episode, Riker, Geordi, Worf, Data, and Pulaski are playing poker. Pulaski puts two neat stacks of chips in the center beside some chips in a pile. It then shows Worf putting similar stacks in the center but Pulaski's stacks are not visible and they should be. Then when Worf wins the hand, the camera is showing a wide shot of him pulling the chips towards him and you can see his and Pulaski's neat stacks of chips.
Continuity mistake: In the scene where Data is brushing Timothy's hair into a copy of his own hairstyle, he stops, kneels down and asks Timothy "Timothy, are you having bad dreams?" In this shot there is a big tuft of hair on the right side of Timothy's head that sticks straight out. When their conversation is over and Data stands up in the wider shot, all of Timothy's hair is in place.
Encounter at Farpoint (1) - S1-E1
Continuity mistake: While trying to escape Q, the Enterprise fires eight torpedoes, but only five explode. If all detonated, the last three weren't shown, but Tasha reported detonation after only five. (00:15:30 - 00:17:10)
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.