The fact that he could admire The Woman, and appreciate her cunning was something I felt humanized him. Sherlock Holmes knew he wasn't the best, yet, he was not a particularly humble individual, yet he was smart enough to know that he had flaws and here were people better than he was out there.
I think the value he placed on others that he deemed worthy made him the both likable and great.
And it is because of this I felt that the BBC version of Sherlock was one of the more faithful adaptions of that brilliant detective. But there is a bit of a balance problem that I have with it. I feel that Irene Adler was both over and under represented as herself in that series.
I felt that the show cheapened her. She showed up way more than necessary, for no purpose whatsoever.
The Woman beat Sherlock based solely on wit. It had none of that sexual undertone that was built into the show that I found particularly insulting.
She didn't seduce him.
She beat him.
And Doyle was smart enough to write a character that didn't win by luck, she beat him with guile. However she wasn't interested in seeing if she could lose. So she never came back.
I read the complete adventures of Sherlock Holmes when I was in 6th grade, and Irene Adler shaped how I view women, then and now. It's interesting to me how adaptations of Irene Norton, né Adler, a woman who loved her new husband so much that she would never use the incriminating photograph she possessed because it would harm them both, depict her as this criminal in love with Sherlock Holmes.
Aside from that gripe it is a good show. Though if I am to pick nits, I might as well be thorough.
I hate how he is perceived as bumbling- and I'd say it's because of the Nigel Bruce characterization, except that Agatha Christie apparently at least in part based her Captain Hastings character on Watson and he was an absolute bumbling idiot.
One of my least favorite characters ever.
Watson was a normal guy working with the tools he had and generally going an awesome job. Watson added a lot to the stories.