@goddamnironman: you are correct on 1 and 2 but it is still quite thin as an explanation... as for 4 they should have at least mentioned something... anything! as for 5 when he crash landed shouldn't his next move, be his way of going to the Stark tower? doesn't he have a spare suit there?
Ah! I remembered another one! So when Rowds asks Tony for a suit at the battle towards the end, he said that only he could fly them they were coded to his dna. But Adrich flew one. Pepper flew in one (okay maybe he had made some special parameters for her) the President flew in the Iron Patriot. That line was intented for laughs and that was the problem, they decided to go with funny and over the top action in at the expense of plot... It could have been great. the Mandarin is an amazing villain and they they used was pointless and for what.. for laughs!
The armor's Tony said were coded to him were those ones in the hidden bunker. Aldrich and Pepper both flew in Mark 42, the new experimental armor, that wasn't on the scene when Rhodey asked for an armor. And the president flew in the War Machine, which AIM upgraded to the Iron Patriot (that's how tony viewed those Extremis experimentation videos in that Fanboys' trailer. Therefore, of course it's reasonable to believe AIM could hi-jack it, and abduct the president by putting him inside the armor and remote controlling it.
I swear, pay attention to the movie, instead of just being so quick to rag on it.