This is all great advice, but the one thing I'll add is that I started doing this with movies and television before I started with books (well, except for character, which I've been analyzing since I was a wee thing). It's easier for me to see the flaws and strengths clearly, because (1) reading books is my first love, so I tend to be more forgiving, and (2) I tend to read as fast as my brain will allow, while filmed media force me to follow along at a slower pace. I'm still better at analyzing movies, which employ a few different techniques for delivery, but with the same basic parts as novels. Prose, narrative voice, etc. are the biggest difference, so I tend to read books with an eye for those.
Not only do I analyze what doesn't work, but when other people don't like something I do, I listen to them and figure out why they don't like it. Because, see, I don't think good storytelling is all that subjective, it's just that different people prioritize different aspects of it. Forums are good for this.
Good sites for critical analysis of television and film are
TWoP.com and
Redlettermedia.com. The first has a very analytical forum culture, and the second funny movie reviews with an eye towards deconstruction. I strongly recommend RLM.
For me, it helps a great deal to talk to another writer who's read the same story. We do it in private, picking apart what we like and what bothered us. For me, the most useful stories to analyze are the ones that we call "almost good." A really bad story needs no analysis. A super good one seems to have a smooth surface that's hard to penetrate. But one that has a promising start then a flat ending, or good characters but clunky language, or good start and ending but a saggy middle--those I can learn from.
Not that any learning is final. I seem to have to keep learning and relearning with each thing I write.
This. My husband and I do this all the time. He's good at analyzing plot, structure, and perspective; I'm good at doing so for character, setting, and conflict. We learn a lot from each other.