First of all, Sherlock Holmes stories are only somewhat about the mysteries and his deductive process. The real reason they've stood the test of time is because of Sherlock's attitude (which considering the success of House, is still wildly relevant and popular today), and the combination of Sherlock and Watson (and considering the number of buddy action/comedy/whatever movies, this is just as wildly popular). The detective elements, and particularly Sherlock's near magical deductive abilities are also important features, of course, but really it is the combination of the three that sets Sherlock Holmes apart from the CSIs and other derivatives of it.
That said, of course Sherlock Holmes is relevant. First, why do you assume that modern science and forensic knowledge makes Holmes obsolete? Holmes was at the cutting edge of his time, doing research and investigating things and approaching most things in a very scientific manner. A modern Holmes, like the one on the tv show Sherlock, would take advantage of all today's tools, only combine them with his uncanny focus, memory, and intelligence to push well beyond what an ordinary person could achieve. And why do you imagine police would be more competent today than they were fifty years ago, or a hundred years ago, or in Sherlock Holme's time? Technological advances are great, but they still require people capable of using them, and the more technology we get, the more memorization and knowledge it requires, the more people involved in the process, and so on. While it takes the CSI and NCIS and Criminal Minds or whatever other shows an entire team of people to solve a crime, Holmes does the same thing by himself, with only some assistance from Watson. I find nothing strange or unrealistic about that, given the capabilities of the character.
Anyway, I've actually enjoyed Elementary, though maybe that's just because Lucy Liu is really hot, and any Sherlock Holmes is better than no Sherlock Holmes. But Elementary is simply fantastic, and fits hand in glove with what I described above. A Watson that isn't a bungling idiot but a capable and likable guy, a Sherlock Holmes that uses all the advantages of modern science and technology, and so on.
Oh, and one last thing, a lot of Sherlock Holme's cases had nothing to do with the police at all. He became famous, and people came to him rather than the police, especially if they wanted to keep things quiet, didn't have sufficient evidence for a police visit, and so on. So quite often the police were simply never given a chance, even though they likely would have succeeded as well, eventually. That part can certainly stay true in modern times as well.
I love that show-brings back's so many fun and happy memories ^_^
