I can now honestly say that I love Mulholland Drive while embracing the ambiguity of the claim: I love both the road and the movie. Though, to be honest, I've always loved the road, and still love it more.
But, when I first watched the movie, I didn't quite love it -- I probably hated it. So, I'm going to write about my change of heart, without any purposeful spoilers, but, just to be safe, I'll give no spoilers of any type until after the fold. And, even then, I don't think I'm really giving spoilers at all.
My purpose here, though, is not to give a theory of the film or even to answer a question. I just want to ask a question: why do people love movies that don't make sense?
I don't have an answer to that myself, so this post is really just a very long question, which has a tl;dr version that I've already given. But, of course, being a philosopher, I also have a much too long, but you can read if you like version coming right up.