He gets a specific one when he gets caught in an Extremis blast. He's on his back, barely conscious, badly wounded, and his first reaction is to point at the dog tags nearby, the one thing he knows Tony will need to look for to work things out.
Rhodey kicking ass and saving the President by just being a Badass Normal. Tony is not the only one in the movie who proves he doesn't need the armor to be a hero.
Not just that, before that Killian tries melting him out of the armor. Rhodey is in terrible pain but begging the armor not to open... and then when he sees the safety failsafes will make it open anyway, he gets ready, and as soon as the Iron Patriot armor pops open he comes out swinging. If not for Killian breathing fire, Rhodey could probably have saved the day right then and there, with his bare hands.
At the climax, Rhodey asks for an armor suit, and Tony tells him that he isn't calibrated for any of the Iron Man armors. So what does Rhodey do? He goes and takes back his stolen suit.
Fridge Brilliance gives one to the President. When the Mandarin gives the ultimatum to call him or he will kill a man on live television, the President dials, but the Mandarin never answers the call and shoots the guy anyway. We later learn the Mandarin/Slattery is working off a script, and he looks nervous as the phone rings.They didn't expect the President to actually call, and had no idea what to do when he did. Screw the Rules, I'm Doing What's Right indeed.
Tony, only partially in armor, takes down Killian's men with a pistol, some repulsor blasts, ingenuity, and bouncing around like crazy with whatever thrust he can muster.
Pepper finally getting her chance to show us her awesomeness in full display by saving Tony from Killian in the climax. Without missing a beat, she backflips off of Tony's knee, drags her white-hot fist through an Iron Man suit and brings it to the ground, rips off an arm and sends Killian flying, then assembles the gauntlet on her arm, removes a tankbuster missile, and blasts it, obliterating Killian.
The Stinger: Just when you thought they weren't going to mention the Tony Stark/Bruce Banner bromance from The Avengers...
Tony saved all of the surviving passengers and crew of Air Force One! JARVIS said the suit can only carry four people. There are thirteen falling. Tony guides each of the falling people into a skydiving maneuver and uses an electrical current to lock their grip so they can't let go of each other. They reach the last survivor just in time for Tony to turn up the thrusters and land everyone in the water. Then it becomes a Crowning Moment of Funny when he turns to fly away and gets hit by a truck, breaking apart the pieces of the hollow armor.
It's especially awesome in that they used a real skydiving team to pull it off. No CGI.
The passengers themselves deserve a mention. They're falling thousands of feet to their impending death, but as soon as Tony tells them to grab each other, they do not hesitate or panic for even a second, helping Tony and helping themselves in saving all their lives.
Tony vs. Mandarin/Killian, as he keeps switching between armors and his opponent keeps up, Terminator-style.
Some of Tony's more specialized armors get a chance to shine, such as a Hulkbuster-type armor and an armor equipped with twin piledrivers.
The closing lines alone:
Tony: So if I were to wrap this up tight with a bow, or whatever... I guess I'd say, my armor? It was never a distraction, or a hobby. It was a cocoon. And now? I'm a changed man. You can take away my house, all my tricks and toys. But one thing you can't take away? I am Iron Man.
Tony's initial assault on the Mandarin's compound. He's lost most of his resources at this point, and can't power his suit back up in time. So he puts together an assortment of Improvised Weapons and plows through a dozen armed guards effortlessly.
Maya pulling a High Heel-Face Turn and threatening to kill herself if Killian doesn't let Tony go. Sadly undercut when Killian decides to cross the Moral Event Horizon and just kill her himself.
President Ellis is no coward. He faces down the stolen Iron Patriot Armour that has just plowed through his entire security detail on Airforce 1. He has nowhere to go yet he grabs a gun, and when that fails, he says, 'go on, do it'.
Once he was freed, the fact that he was wearing the Iron Patriot armor for a few seconds was pretty cool.
Rhodey: You look damn good, sir.
While the Mark V/Suitcase Armor was based on the fan-favorite Silver Centurion, a proper S.C. armor pops up for the finale and disarmsKillian.
JARVIS has several awesome moments in this film. From saving his creator from drowning to rebuilding entire crime scenes to coordinating 40+ Iron Man suits in a full-on war while simultaneously putting one in front of Tony whenever he might need it, JARVIS showed that just because he's an AI, doesn't mean he's not a dangerous force to be reckoned with.
Hell, the entire final battle. Every Iron Man suit Tony's built vs Killian's suped-up Extremis lackeys, who they then proceed to utterly thrash. The only times that the bad guys can take one down is actually piling on top of it and using superior numbers, and even then JARVIS does his best to take the suit's destroyers down with them by making them kamikaze into places where they'll do a lot of damage.
A noteworthy moment during said final battle would be the piledriver-equipped suit knocking two Extremis troops into the air so that another suit can blast them in an impressive display of teamwork.
This exchange before said final battle just sells it:
Tony: JARVIS, target all Extremis heat signatures, disable with extreme prejudice.
Trevor Slattery may be a washed-up, drunken, drug-addicted former actor but you have to give the guy credit - he gave such an awesomely chilling and convincing performance as the Mandarin that he had practically all of America quaking in fear of him. At the end of the movie, he even seems to have gained a fanbase from his performance.
A marketing example would be how the big twist of the movie was carefully covered up by the marketing campaign. Specifically, how Ben Kingsley's Mandarin is just an actor and how Killian was behind everything. The trailers, interviews, and even the merchandise suggested that Killian was nothing more than a background character, making it that much more surprising when it's revealed that he's the antagonist. While this caused a Broken Base, there's no denying that it took marketing genius to keep that information under wraps in an age where spoilers are spread so easily.