The Royale - S2-E12
Trivia: In this episode, Picard is studying Fermat's Great Theorem, and says it has remained unsolved for 800 years. Five years after the episode was made the theorem was proven, by Andrew Wiles and Richard Taylor from Princeton University (their proof is not the same as Fermat's though, as they used modern methods Fermat did not know of). In the Star Trek universe, this was referred to in an episode of Deep Space Nine, and is considered as a subtle correction for Picard's statements.
Trivia: Closed captioning, in its infancy in the 80s, often dropped words and letters by accident. In the original broadcast of this episode, the captioning of Riva's line, "We could dine together," lost an N, resulting in a rather bizarre exchange. Riva: We could die together. Troi: I'd like that.
Trivia: As Picard argues for Data, the wall behind Maddox can easily be seen as the forward wall and viewer of the Enterprise Battle Bridge, re-purposed for this episode.
The Royale - S2-E12
Trivia: When Captain Picard is reading Hotel Royale in his ready room, he comments that the book's first line, 'it was a dark and stormy night', is "not a promising beginning". This line is actually the first line of Edward Bulwer-Lytton's Paul Clifford; the line has become so clichéd that it frequently appears in satirical works to denote humorously incompetent or overly melodramatic writing.
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.