I think some of you are making the mistake of projecting the books onto the movie. The movie character, is CLEARLY an E.
I think ENTP is settled for Holmes (in the movie version).
I also agree with JJ that Watson seemed ISFJ. Strong, dependable, responding, informing, affiliative, structure over motive, niether overly sensate or intuitive.
The girl was probably the hardest person to type. I could see her as JJ's twin (ENTJ ). Though sometimes STP crossed my mind (only briefly).