This issue is proving especially important to me at the moment, as I'm trying to write a literary mystery novel. I want plot and character to be equally important, and indeed to be bound together inexorably. Reading Conan Doyle has helped me discover that this is not only possible, but perhaps even necessary for delving into the true nature of mystery. Before attempting my novel, it seemed to me that mystery writing was primarily about plot, and by plot I mean a series of circumstances. A is in line to inherit B's money, but B has fallen in love with C and altered his will, making A the prime suspect when C is found floating in her nightgown in the lake. None of these characters is interesting, beyond their singular motives, which correlate to their functions in the plot: A is greedy (or desperate), B is blinded by love, C...well, C is a victim. D, the detective, comes in and puts the pieces together, because D, whatever her personal quirks, does her job expertly.
Now, Holmes is that quirky expert in Hound, but thus far, it's Watson whom we see doing most of the investigating. And here, he makes a mistake. Not only because the plot requires him to do so, although it does, but because of who he is.
After the conversation which I have quoted about Barrymore, Sir Henry put on his hat and prepared to go out. As a matter of course I did the same.
"What, are you coming, Watson?" he asked, looking at me in a curious way.
"That depends on whether you are going on the moor," said I.
"Yes, I am."
"Well, you know what my instructions are. I am sorry to intrude, but you heard how earnestly Holmes insisted that I should not leave you, and especially that you should not go alone upon the moor."
Sir Henry put his hand upon my shoulder with a pleasant smile.
"My dear fellow," said he, "Holmes, with all his wisdom, did not foresee some things which have happened since I have been on the moor. You understand me? I am sure that you are the last man in the world who would wish to be a spoil-sport. I must go out alone."
It put me in a most awkward position. I was at a loss what to say or what to do, and before I had made up my mind he picked up his cane and was gone.
But when I came to think the matter over my conscience reproached me bitterly for having on any pretext allowed him to go out of my sight. I imagined what my feelings would be if I had to return to you and to confess that some misfortune had occurred through my disregard for your instructions. I assure you my cheeks flushed at the very thought. It might not even now be too late to overtake him, so I set off at once in the direction of Merripit House.
I hurried along the road at the top of my speed without seeing anything of Sir Henry, until I came to the point where the moor path branches off. There, fearing that perhaps I had come in the wrong direction after all, I mounted a hill from which I could command a view—the same hill which is cut into the dark quarry. Thence I saw him at once....
Watson's mistake--disobeying Holmes's instructions to accompany Sir Henry everywhere--is plausible, because it fits his character: from the beginning, we've seen that he's polite, a bit meek (especially in the presence of Holmes), and even a little insecure (a hazard of working with Holmes). Thus he's easily put off by Sir Henry's entreaty not to be a "spoil-sport." But just as quickly, he feels terrible about letting Sir Henry get away, and imagines having to confess his error to Holmes--reactions that are also consistent with Watson's character. To fix his mistake, he runs off after Sir Henry, gets lost, and finds himself in a position to witness a telling interaction between Sir Henry, Miss Stapleton, and her angrily gesticulating brother.
So here's my point: a lesser writer, or at least one less concerned with character, could still have arranged for Watson to stumble upon this meeting. Watson could just decide to mosey off to a nearby hilltop of a morning, thinking Sir Henry asleep, and unexpectedly come upon the rendezvous. But this plot point is brought about, instead, by Watson's distinctive and very human nature. He falters, and then, alarmed at his failure, rushes to amend it. Yes, overall, Watson's discovery still reflects the operations of chance, which, in the case of a novel, means the author's hand. Yet we don't feel the author's hand here so strongly, because he lets Watson, or Watson's humanity, lead to the discovery.