Wolverine and the "Nuke"
Problems:
1. Boots, pants, belt, skin, and hair all appear undamaged
2. Intact debris only feet away
3. Nothing is on fire
The idea of the nuke being only a napalm bomb with a sonic component to the blasts sounds more reasonable as there are very few comic book characters who should be able to survive a nuclear explosion at ground zero and Wolverine is most definitely not one of them.
Regrowing Organs/limbs
While the portrayal of Wolverine's regenerative abilities when it comes to entire limbs or organs, I would not dismiss the possibility out of hand. Given the fact that his healing factor can rather easily accelerated or decelerated by writers to fit their story, this is a difficult question to answer. Right now I would say that both are at least possible.
Joints
While 616 Wolverine has shown that his joints appear to be "unbreakable" as his skeleton in various feats, Marvel has never addressed how this is possible in a satisfactory manner to me. As far as I know there was never any mention of radically altering Wolverine's bone structure before its bonding with adamantium nor has it even been mention that his connective tissue was fortified in any way. Thus we have feats with no explanations for them, which may be fine or complete PIS according to your feelings on the matter.