I haven't read the actual Sherlock Holmes series in ages, but in this series (which is quite brilliant) Sherlock strikes me as a heavily ingenious ISTP. Such a good example of a crazy intelligent S, since Ns tend to get that smart guy cliche. At his core, this Sherlock is a thrill seeker who notices the littlest details to help him figure out not only crimes but people instantaneously.
Watson, INFJ seems about right. Someone who pulls Sherlock away from his almost (self-described) sociopathically detached outlook as much as he can. He sees a body as more than a thrill or a game in both an N way and an F way. At least to me.
Mycroft is an I(?)NTP. He's fine contemplating, but he's not so happy with, as he puts it, "legwork". Why I'd lean I: Mycroft was, I think, an I in the original series and tends to keep very limited company and comes off as not especially outgoing here.
Absolutely love this show. I've been a huge Sherlock Holmes fan most of my life and Benedict Cumberbatch is now my second fav Sherlock Holmes after Jeremy Brett. Which is saying a lot. The modern update is generally brilliant and the casting and scripts are awesome.