Near-divinatory levels of insight about his environment are basically Holmes's superpower: the important thing is the upshot, not the realism of the process. IIRC there's a lovely bit of Albert Campion, or possibly Lord Peter, in which the detective bitches about how Holmes's insights should really be wrong a lot of the time. As with any superhero, you're supposed to suspend disbelief and go with it. At least it isn't laser vision :>.