Nakomi/woman at the end is the only real thing that baffles me. The body switch is confusing, but at least I get how that could make some kind of sense, but Nakomi is still just randomsauce.
Rand, being 400+ years old and having memories from the Age of Legends, does know more than an, at most, 70-something scholar in the end of the Third Age.
It's entirely possible that the small part of The Dark One present in the world is the little bit of the True Source that the Dragon used to seal him away.
I'm still wondering about how, exactly, Rand and Moridin switched bodies.
I believe that Rand burned himself out, which is why he's unable to channel at all. I think it was briefly mentioned that he was holding too much of the Powers. As for the pipe, that still baffles me. I kind of like the...