Rationalism v. Superstition
One of the novel's primary themes is the conflict between rationalism and superstition. Much about the hound case suggest occult explanations, but Holmes steadfastly refuses to consider such possibilities. It is easy to understand why many turn to such explanations. It is not only that the people of the moor are primitive, tied to a folk religion. It is also that there is so little evidence with which to construct a rational explanation, other than the myth of the hound. Even a man of science - Dr. Mortimer - is driven to consider such occult possibilities.
But Holmes represents the power of the intellect: he possesses sound reasoning abilities and sharp observation skills. He tends to approach problems from a scientific standpoint, avoiding religion or superstition as causes. Instead of turning to implausible possibilities, Holmes seeks for clues where others have not looked. The idea seems to be that there is always a rational explanation; the evidence just might not always be easily observable. But the first step towards finding that evidence is to prize the power of the rational mind, and refuse to consider irrational possibilities.
Objects as Historical Artifacts
In many Sherlock Holmes adventures, objects play a significant role, since Holmes uses them to deduce truths not immediately observable to others. In The Hound of the Baskervilles, this theme is clear from the first chapter, in which Watson and Holmes each work to interpret Dr. Mortimer's walking stick. What Holmes illustrates is that every object has a history, which can be used to construct a story of its life. The larger implication of this approach is that humans always leave traces behind; one must simply know how to read those traces.
In context, this approach is particularly relevant since Scotland Yard (London's police) had recently begun using fingerprints in its criminal investigations. Obviously, the assumption with such technology is similar to Holmes's: people leave their unique marks everywhere. By learning to identify what is unique about an object (or the person who used it), one can eventually find a criminal from a crime scene.
The Holmesian methodology
Largely because of his singular detective method, Sherlock Holmes has remained a popular figure even today. That method is central to the story of Baskervilles. In interpreting it, one is lead to many questions: How does Holmes actually solve his cases? Is there a single method which he applies in all instances? Is it realistic? Is it replicable? Because he does not narrate the novel himself, Holmes does not exactly illustrate his approach to us, and we are left in large part to interpret it. There are two important elements to consider. The first is his method of observation, detailed in the "Objects as Historical Artifacts" theme section. The second is that Holmes considers multiple possibilities at once. Occasionally in this novel, he gives us an indication that he had to consider and then dismiss dead ends. Therefore, one could say that Holmes's approach is not as clean-cut as it seems at the end of the story, but instead is built of several guesses and false starts. In other words, it is arguably less scientific - making a hypothesis and then testing it - and more medical - diagnosing a problem by eliminating possibilities based on symptoms. No matter how one articulates the nature of Holmes's method, it remains one of the enduring themes of this novel and of Doyle's other Holmes stories.
Facts and Assumptions
Perhaps the greatest antagonist to Holmes's method is the human tendency towards assumptions. What most people do is study a scene in its entirety and then interpret its basic type. However, Holmes assumes nothing; he might identify the 'type' of scene he is studying, but then spends his energy looking for the particulars that make the scene unique.
The problem is that appearances can initially be deceptive, as a person might too quickly jump to conclusions. For example, Dr. Mortimer sees a paw print near Sir Charles's corpse, and concludes that there is truth to the hound legend. When Holmes instructs Watson to report only the facts of the moor, he is attempting to stop the man from integrating assumptions into his observations. Though this is almost impossible advice to follow - since Watson is naturally influenced by the atmosphere and his conjectures - he does use this understanding to conduct his own detective work, which yields dividends like the information about Laura Lyons. Holmes's suggestion seems to be that one must study the fact in itself, and then conduct guesswork based on it.
Urban life v. country life
The Hound of the Baskervilles explores on several occasions the distinctions between city and country lifestyles. In particular, one can observe the conflict in Watson himself. Whereas he is easily able to eschew supernatural explanations while in London, he finds himself more driven towards those possibilities when isolated in the country. Whereas the bustle of the city allows for a scientific approach, the atmosphere of the country dissuades it. In no uncertain terms, Watson calls the people of Devonshire primitive, and Baskerville Hall an evil place. Though certainly not a nuanced portrayal, Doyle's picture of country life is provocative and clear.
Moral, legal, and social order
The novel's story is largely contingent on the existence and legitimacy of established order. It is important to note that professional police forces did not exist in London until the 19th century. As the city grew, crime became more concentrated, and citizens needed better protection. Holmes takes the importance of such protection for granted. However, it is important to note that the law is rarely capable of the actual detective work in Holmes stories; that is certainly the case here. What drives Holmes, then, is a basic sense of morality. Even when he uses deceit, he does so for the ultimate good of catching the criminal. No matter which type of order Holmes employs, it is clear that he believes in the inherent value of such order.
Genius
Though it is hardly central to the story, the novel does explore the nature of genius. In particular, Holmes's attitude towards Watson suggests the idea that genius does not empathize with others. Not only does he use Watson as his pawn - sending him out to Devonshire as part of a ruse - but he also shows little sensitivity towards Watson's offense when he finds out. Instead, Holmes expects Watson to accept the intellectual necessity of that ruse. Holmes's lack of friends, his obsessive nature, and his general emotional distance all suggest that a true genius has little use for the trappings of ordinary life.
