On the logic of Sherlock's world

As I alluded to back in my review of Sherlock (the third season that is) I was more than a bit disappointed in how the season's "grand villain" was handled because it just didn't make any logical sense to me. Logic is a bit part of the setting for any story, it determines how the world works, how character's react, what is and isn't possible (which informs the audience of what may or may not happen) and when you have a story where this isn't made clear usually it becomes a plot point in and of itself. So when Sherlock, which had already done a good job at establishing that it was set in a world like ours, just one with a genius detective in it, started to have it's villain act differently, well, it meant that the world stopped working for me too.

(spoilers ahead)