Keep in mind, Arthur Conan Doyle's Sherlock Holmes stories are all in first-person point of view, told from the perspective of Dr. Watson. In that respect, the point of view is always limited. Watson does not have access to Holmes's inner thoughts or perceptions, or, at least, he has access to nothing beyond what he might infer or, as is so often the case, what Holmes himself might reveal to him. Such is the case where "The Adventure of the Speckled Band" is concerned, as well.
Quite possibly the most powerful and memorable example of this dynamic can be found in the story's climax, where Holmes and Watson spend the night waiting in darkness in Helen Stoner's room. Note that before they depart, Holmes expresses his misgivings about bringing Watson along, noting the danger they will be in. Later, as they settle in to wait, Holmes warns Watson against falling asleep, noting that his "very life may depend upon it."
By this point in the story, Holmes has already largely solved the nature of the murder, even if Watson remains unaware. This dynamic actually lends the scene much of its suspense: Watson does not know what it is that has Holmes so worried in this instance, but the very fact that Holmes would offer such warnings speaks volumes as to the danger the two are facing. All the while, Watson (much like Doyle's readers) is left in ignorance as to what that danger specifically entails.