mt, that reference is to a yoga site.

In yoga, you are not breathing air, you are ingesting prana, the fundamental life force (according to Hinduism anyway). If this was meant to be a religious discussion, please allow me to withdraw my previous comments.

Mouth-air and nose-air get mixed near the back of the mouth. I'd be grateful for any theories on how this would affect the efficiency or quality of air going to the lungs.

The pressure drop breathing in through the nose is negligible, and the energy in opening and closing your mouth every breath is unlikely to be significant either. Both of these would favor mouth-breathing anyway.