The observational acuity of which Holmes is so proud is epistemic nonsense. Invariably upon first meeting a prospective client, Holmes will recite to an amazed Watson after the person leaves all that he learned about the person from the scuff marks on his shoes, the calluses on his fingers, and so forth; and this is taken as a sign of Holmes's perspicacity.How Watson, on his modest salary, could afford to have a window in his bathroom is another story. The Victorian townhouses here look pretty cramped, and even some of the more spacious floor plans of the era had only windowless water closets. But that's all I could find after a brief bit of googling -- perhaps the right configuration existed somewhere in London. Who can tell?
The reductio ad absurdum is Holmes's wowing Watson by "deducing" that the window in Watson's bedroom is on the right side of the room from the fact that the left side of Watson's face is not shaven as smoothly as the right, implying that the sunlight was coming in from the right in the morning when he was shaving. But only if Watson was facing north--and no points of the compass are mentioned--would the window on his right be facing east and thus admitting the morning sunlight. And there's a deeper problem. The sun's position is irrelevant; the window just has to be to the right of the mirror as one faces it for the outside light to hit Watson's right cheek.