In one of the threads last season, I suggested that "Jessica" wasn't a schism of Nichole's personality at all, but the actual projection of Jessica's spirit into Nichole's body. Someone had the same idea last week, applying it to Peter's "death" by megaton explosion. Nathan got away in time to not be burned, but Peter "died" and the power he absorbed from Nikki wasn't just her strength, but Jessica's projection ability, as well. "Dead" Peter jumped inside Nathan's mind, but apparently the body came back to life, and Peter was then either mindwiped by the Haitian or his psyche actually left, to a large extent, so no memory of the last four months, or anything, really.
Nathan did see a horribly-burned Peter staring back at him, and he does from time to time, hence his not being a senator, and living out of a bottle.
Now for the kicker.
"Dead" Peter is projecting out and either materializing to destroy the Old-schoolers, or manifesting telekinesis to do something physical. Nathan has no idea, really, what is happening, but is experiencing blackouts when Peter goes into action.
A possibility that just occurred to me, given Jessica's MO of acting when Nikki's in trouble, is that "Dead" Peter is not coming out of Nathan at all, but is using Nathan's flight and several of his own powers that are strictly mentally-operated to act on Nathan's subconscious revenge-fantasies.
Other Things.
I can handwave the Nathan and Matt not really knowing each other, because any meeting they had was necessarily brief, it's four months after that, and they've both had a lot of upheavals.
Mohinder never met the Haitian, until the virus-curing.
Conjecture: Mohinder has a power, a weaker variant of Alejandro's and Linderman's. He said last season that sometimes babies are born with the antibodies their siblings need. Even a distillation of Mohinder's blood shouldn't work on anyone not related to him in the strictest sense, unless he, too, is special.
In one of the pre-season teasers, Hiro flat-out says that Kensei has power, too.
Hiro has not mastered his powers, and still makes mistakes. It is quite possible that he was startled enough that he just couldn't react in a good way. I think that Hiro and Kensei are, together, the root of the Takezo legend. Hiro has only recently lost his love, so Kensei can have her, and seems to want her. Hiro can provide many of the feats attributed to the legendary hero, and Takezo has some sort of power that may come in handy, that way, too.