1. Sherlock makes the same mistakes over and over again.
From the first season to the fourth, Sherlock behaves destructively over and over and over again. As the viewer, we never see consequences of these actions. For example, his drug use causes no health complications. He mistreats people and they keep coming back to him because of his superior intellect. Is this realistic? I'm not sure it is... Putting Sherlock on this pedestal makes it all too easy for other characters to forgive his mistakes, no matter how harmful they might be.
2. The series does not positively portray women.
First of all, the Conan Doyle books definitely do not portray women in a positive light so one might think that it isn't unreasonable that the Sherlock BBC series does the same. HOWEVER, BBC's Sherlock occurs in 21st century London!! Is that not reason enough to include strong female characters in the story?!?! BBC's Sherlock seems to take these female characters and "use them to propagate stale gendered archetypes." For example, Irene Adler tries to use her sexuality--her naked body-- to provoke Sherlock Holmes. Furthermore, Adler's ultimate downfall is her inability to separate her romantic feelings about Sherlock from the job she needs to get done. Adler goes from being Sherlock's equal on an intellectual level to a woman who lets her feelings get in the way. Other characters such as Molly, Mrs. Hudson, and Mary don't have much of a back story until much later on in the series. They exist in Sherlock's universe, not as people with agency of their own.
3. How many unresolved plot lines can one show really have?
It's one thing to leave a show with a huge cliff hanger at the end of a season. It's another all together to leave that cliffhanger and then neVER EXPLAIN IT. At the end of season two, Sherlock fakes his own death. Now, you would expect that the beginning of season three would show you exactly how Sherlock managed to do this. However, this was not the case. Instead, the creators chose to illustrate several different theories as to how Sherlock might have accomplished this feat. As a genuinely curious audience member, I would LOVE to know how Sherlock actually did it and I was left unsatisfied by the lack of resolution. In general, the show seems to have a lack of plot resolution AND little plausibility. I would love to think that someone like Sherlock could exist but with what he has gotten away with, that seems super unlikely.