I don't know why the world is obsessed - actually I have doubts whether the "world" is, I still have to find somebody in real life who's even seen the show.
But what fascinates me is the combination of great characters (I've always like Sherlock Holmes, read the book as a teen, saw the movies when they were on tv, without being an active fan and I very much like Benedict Cumberbatch's interpretation), stunning visuals (I love the behind the scenes documentaries of how they did some of the work) and less than perfect writing (to put it mildly).
Not the dialogue, there's some great lines. But the plots leave a lot to be desired and the technical and scientific details are at best implausible or even simply wrong - I'll be spending hours re-watching the episodes trying to find all the problems ;) Of course, ideally I'd have Sherlock here to dissect the show with (now wouldn't that be fun!) but as that's not going to happen, I hope you won't mind standing in for him.
Having just watched HBO's The Wire, which critics say is excellently written, realistic, all the details right (not knowing anything about the drug scene or dock workers in Baltimore, I wouldn't know - it certainly seems real), I can say that "bad" shows are a lot more fun. They make me think, check up on things, try to find fan fiction with better stories, find a forum to discuss things... Whereas, when the authors have done a good job, there's nothing left for me to do but watch.