The writers of this show are totally stupid. Kensai/Adam did not age over a gap of several hundred years, presumably due to his ability. Why did they not think "hey, Hayden pannetiere (Claire) is going to get older as the seasons go on. giant plot-hole ahoy." Seriously if I can see this as someone who watches the show, contemplates it for a bit then forgets about it for a week, why can not they - who are payed to think about the show all the time?
Okay, the problems I had were directly related to one episode and were because they were poorly exhibited, this whining is just a matter of you not exhibiting the slightest bit of petience. Hayden is eighteen right now. If I shave, I do not look any different than I did at eighteen a full five (Almost six) years later and I don't have the benefit of a makeup artist. Between Epiodes I and III of the new Star Wars trilogy, Natalie Portman barely looked like she aged and that was across a span of about six years. Do you really think that this show, or even Hayden's casting in it, will go on so long that Claire's potential aging will ever be relevant? Hell, if you look back to Five Years Gone, the idea of her not aging actually wraps up a potential continuity error in her not looking any older.
From there, we also have the possibility that their powers are not exactly the same. Maybe she does age and Adam doesn't? Or maybe she won't survive the season? While I find that unlikely, considering last season's track record who really knows?
Also what is with peter having DL's ability, he went no where near him at the end of the last season, then DL died presumably from the bullet wound (interesting that the paramedics can save Parkman who took 5 bullets to the chest, but not DL) If he has that ability from the opposite side of kirby plazza he should also have Micca's, Molly's and Eden (the siren girl who died early in season one)
Watch the season one finale again, you're obviously not paying attention. D.L., Micah and Nikki were all at the plaza with Peter. They were all at about the same distance from Peter as Ted was when Peter first started mimicking his powers. He probably does have those other powers but isn't aware. All three of those are powers that are actively triggered and ones he's not likely to use unless prompted. Considering he's been either doped up or amnesiac for most of the four month gap, he's had no reason or time to use them.
In terms of D.L., maybe you should, y'know, show some patience or pay attention to details? Detail one: they clarified it in the very next episode (Four Months Ago, last week's episode). We know how D.L. died and it wasn't from that gunshot from Linderman. Beyond that, anyone with an eye for details could tell you that he died later on anyway. Look at the season two premiere again. D.L.'s gravestone says 2007. The season one finale took place in early November, 2006. Even if he HAD died from that, it's not the amount of bullets, it's the location and the timing of the police. D.L. was walking around for a good half hour after getting shot, time he would be spending bleeding. Cops and paramedics showed up shortly after Parkman was shot. From there, we also have the matter of location. Rapper 50 Cent was allegedly shot like nine times and survived while many others bled out from one gunshot wound. It happens, deal.
Another thing, when will they get on and tell us what the previous generation of heroes' powers were. We know Linderman could heal, Parkman sr could manipulate minds, Bob can turn things to gold (though if it is alchemy -transform other metals into gold - or midas touch - transform anything, including humans, into gold - is still unclear.) But we haven't had any indication of what Kito, Charles, Angela, her husband or any of the others can do.
Maybe they'll tell us when it's relevant? For one, Angela's powers are heavily hinted at in the episode you just watched. Do you really think Peter suddenly remembered details of his past just because some old lady told him to? Either she's got a power similar to the Haitian in terms of affecting memory, or she's got a power of suggestion similar to Eden's (There've been multiple other instances of hints towards the latter, so I'm sticking with that). In terms of others, well, we'll see them eventually. Suck it up and wait or watch something else. A slow burn and dangling plotlines were how season one was handled, if you don't enjoy that manner of storytelling, this show isn't for you.