I told Brandon that I'd get this written, and so now I feel some pressure to. Crap, pressure, man...
In a sense, you can look at each of the Iron Man movies as moments of personal growth for Tony Stark. Iron Man 3 continues that trend nicely.
Every Iron Man begins with the Tony of the begining, showing his faults that are in some way going to be explored in the upcoming movie, basic writing foundation building. Iron Man starts with Tony Stark, orphan idustrialist billionare - who exists a world where he has nothing that stops him, no one who's equal to him, and he's completely self-involved (which, like many people, is more of a suit of armor than his exo-armor ever will be. It keeps him safe from being hurt by people.) The few people who know Tony better than a one night romp in the sack or through the tabloids allow him to get away with the assholery he does only because he's Tony Stark, and they love him. Insert personal transistion through explosion and shrapnel and someone else sacrificing themselves for him, and Tony comes out of it different. He realizes he can do more than live for himself, and he can be more. To some degree I think this is why Pepper and Tony had never gone further than boss/coworker before. Certainly Pepper didn't want to be another notch on Tony's bedpost, nor the but of the office gossip; However I think Tony didn't want to ruin the one true relationship he had with another human being. Iron Man I was about Tony thinking about someone other than himself.
Iron Man II starts with Tony, who is still very much about doing good, but still only in the sense of HIM doing good, by HIMself, which of course through the personal development plot line of Vankov, S.H.I.E.L.D., Rhoady, and of course, Pepper, he learns that sometimes the burden is too is too big to handle by yourself. Which really steamrolls into The Avengers, where a an adjunct to that plot line is Tony figuring out how to be a part of a team without being the biggest, baddest part of it. And, harkening back to Yensin's sacrifice, Tony commits the ultimate act of self-sacrifice for the world. Of course, this is a movie, and a franchise, so of course he survives.
But the best connection between the first two Iron Man movies and the third is through The Avengers. Not even the obvious bits about Tony's insomnia/PTSD from the events in the movie, but I think the core of the movie's plot is straight from a line in The Avengers:
Of course Tony glibly replies to that in the movie, but some part of that question haunts Tony. He spends the nights he can't sleep making decades of suits, and beginging to work with remote controlling them through implants.
Tony is, if anything, overly dependant on the suit at the beginging of the movie. He's dropped his armor, so to speak, internally, and in the process has been scarred deeply in his psyche. The emotional barrier that the first two movies worked to dismantle prove to be the real challenge to Tony in Iron Man 3, and it's probably the best bit of character development of the series thus far.
To watch him have to explain to Pepper why he can't sleep, how he's deeply shaken in a way he's never been before, and scared to lose the one thing he thought he'd never have - love, and respect, from a someone he loves - and how to keep doing something he feels is his duty while keeping that love safe, is telling. That he does so with only minimal joking asides is a testament to how open he is with Pepper finally.
The villians and action scenes are excellent in Iron Man 3, but what has made this series so wonderful is continued in IM3 with the continued growth of the man in the machine, so I'm not going to say much, other than it was nice to not have another suited foe, the Mandrian bit was excellent slight, and the finale with Pepper getting the upper hand was great fun.
But the best part of the movie was, for me, watching Tony out of the suit, finally learning what it means to be a hero. Which will certainly set up nicely for the next Avengers movie.