Alright, just back from my second viewing and I picked up a lot of things I didn't the first time. I blame the 3D and the excitement for this. It was slightly less funny, but I enjoyed more the action, especially the ending.
It seems a lot of you folks did not get everything, or did not pay attention. Understandable, it sometimes goes fast, but there is NOT nearly as many plot holes as you claim...
First off, Killian. I've seen complains about how he has too many motives or so. No he doesn't. His ONLY motive is to sell as many extremis soldier as he can. How ? By creating supply and demand, economy 101. And how is he going to do that ? By using in one hand his terrorist organisation, the 10 rings and their "leader" to create terror, and using his puppet the Vice president in the other hand, to create the need for protection, and therefore justifying the need of extremis soldier. How is he going to put the vice president in the president's chair ? By killing the actual president. That's where the oil tahing intervene. The actual president has apparently made sure some big corporations got away with a massive oil tanker leak at one point, giving the "Mandarin" a pretext to kill him (by oil) that "would look good on TV". Him dead, the vice president becomes president, and his puppet is in place. Now in case you missed it, the vice president acts as a puppet because of his daughter, missing a limb, and probably in the waiting list for the extremis virus if daddy plays nice. All of this by remaining in the shadows. It's actually a rather elaborate plan for a "simple" villain, don't you think ? Does he have a grudge against Tony ? Maybe, but if Tony hadn't declare war to him on TV, he probably would never have taken such dramatic actions. He actually needs him to stabilise Extremis. Since Maya couldnt figure out how to do it by herself. She didn't want Tony dead neither by the way, just his help. Eventually using Pepper as a motivation to make him help by force. Killian killing her was a bit of a dumb move, I'll give you that, but since he got Tony now, she wasn't needed anymore. After that, all his plans went to hell of course, thanks to Tony, which explains why he tried to kill him until Pepper put him down for good.
The charging armor problem now, it's logical that the armors have their own power source, since they can be used without tony inside. His arc was never designed to power a suit for an extended time by the way, just his electro-magnet. Remember IM1 "power his heart for 15 lifetimes or something big for 15 minutes". So while his own arc can indeed power a suit, they need their own arc for prolonged use. And my guess is he's not too keen on using his own arc very much, after nearly dying twice from doing it.
Weak armors : they indeed seemed weaker than in the past. But, notice how the prototype can take a heavy beating when Tony is in it ? The problem intervene while the armors are empty, they somehow are not as strong. Even with this, the extremis soldier can burn at metal melting point temperature, no wonder they can do so damage to the suits. Plain old regular villain wouldn't have lasted a minute against those suits. Look at the people in the plain ! There stood no chance against Savin in the Patriot. And Savin didn't even know how to use the weapons, he only used his palm repulsors, fists and a gun found on a bodyguard.
The Patriot being controlled by Killian : that was already said, AIM worked on it for the branding, like Hammer did in IM2. The armor was locked and inaccessible while on Rhodey, although somehow neutralised (I suspect by frying the circuits temporary thanks to extremis power) but once killian cooked him out, they probably got access to the software and reprogrammed it. Why ? To get close to the president, as a trojan horse. Why put the president in it ? Because the thing is remote controlled by AIM, what is the president gonna do in it ? He's trapped like a rat...
Unfamiliar people using suits easily : they don't. All what Pepper can do is walk in it and open/close the faceplate. She doesn't even know how to activate the repulsors. Walking in it shouldn't be difficult, it's an exoskeleton suit after all, it's designed to help moving... Savin in the patriot now. He's a bit more capable, but he had his hands on it before. Even then, he can walk, somewhat fly, and barely use the repulsors as weapons (he looked surprises after blasting a guy with it). And he couldn't use any other weapons. Why else would he punch people and shoot them with gun if he could fire that cannon ?
Why didn't Tony immediately jumped in one of the 40 something suits in the basement while he was under attack in his house and Pepper had the MK42 ? I strongly believe he was actually going to do that, right until half his house collapsed on the trap door. After that it was inaccessible until the cranes cleared it at the end. It's convenient for the movie plot, but it's not a plot hole... Why didn't one of the suit blow it from the inside ? One, explosion in confined underground spaces don't do well at all for what's inside, two the trap door looks a solid foot thick, and is most likely VERY strong to prevent anything from happening from the outside, and therefore the inside too.
That's all for now, but if you see anything else, please speak out, I'll see if I remember it from the movie. I have a very good eye for details and a very good memory when I want. Careful though, I'm not saying there are no plot holes, just that what most people see as plot holes are not, they just didn't understand or simply missed it.