Not that I have a whole lot to contribute to this thread, but I thought this might be interesting:
After having participated in lots of beginner yoga classes, I had a sense that I was ready for something a bit more challenging. I approached a well-respected yogi and asked her when a person knew it was time to kick it up a notch, so to speak, since I didn't want to let my enthusiasm overwhelm my good sense. I was expecting her to say something like, "When you can perform a double back twist while standing on your head," or something such. But instead, she said, "When you are in control of your breathing." That smacked me right in the middle of my third eye. That comment made me far more conscious of the quality of my breathing during both my yoga practice and my running or cross-training practice. I haven't gotten the full-nasal breathing in my running yet (too many other form things to focus on at this stage), but that's my goal.
However, there are times when mouth-breathing is appropriate and useful. During hot weather, certain mouth-breathing techniques can be used to help cool the body. So, IMHO, there's a place for both types of breathing. The key is to breathe mindfully, consciously, and deliberately, however it's done.