Well, ENTP is something I considered as well, but I think some of you are making the mistake of assuming an outgoing, clever, and funny personality means extroversion. Pay close attention to his motives throughout the movie. Everything he exists for is solving the mystery...unlocking the clues and processing and exploring the data to construct a logical framework. His entire motivations in the movie are based on Ti. Remember the scene near the beginning where he's been sitting in that dark room for two weeks going crazy because he doesn't have a case to solve. He says something like, "There is absolutely nothing of interest out there for me at all." Clearly introverted. An ENTP would be much more concerned with simply endlessly exploring ideas to ever be as good as Sherlock at dissecting the data and doing something with it. Ne serves Ti's ends in this movie, not the other way around. As for ISTP, this is the most likely alternative, but I believe his sensing function is introverted. When he looks at a crime scene he never writes anything down, he internalizes it and recalls it later for Ne's end of exploration. Ne's exploration then serves Ti's end for solving the puzzle and you have a brilliant detective. As for secondary Se...consider that when he perceives something outwardly (Pe) he is quickly running through endless possibilities in his mind (he even vocalizes these sometimes when he "explains" his methods). It's all about exploration, experimentation, and then this gets processed and structured by Ti. The process by which he evaluates external data is a clear Ne/Si combination. Lastly, if you pay attention, inferior Fe is very evident throughout the film, which would seem to disqualify ENTP.