Let me mention again that there are spoilers in this post, so delay your reading if you haven't seen the movie yet. Come back when you have and read this then, it'll still be here. Thanks.
Robert Downey, Jr. - He deserves every dollar of his paycheck. He brought the character of Tony Stark to life the way that no other actor arguably could. He brought humor and gravitas to the role, beyond what was obviously in the script and the pages of the comic book. Iron Man can still work without him, just as Batman continued after Michael Keaton and James Bond survived after Sean Connery. They can even have Iron Man appear in the next few Avengers films without taking off his helmet, so they don't technically need to have him in them and spend a fortune of the budget on his salary, but any further sequels would be at a disadvantage without him. Connery played Bond seven times, so I'd like to see Downey at least tie that as the invincible Iron Man. Hopefully Disney and Marvel can find a way to make it work financially through both profit sharing and merchandising incentives -- actors need to realize that it's in everyone's best interests to keep production costs down in order to maximize profits in the end. The bottomline is that Downey is perfectly cast in this, he is the heart of the Marvel Universe right now, and in every appearance so far he seems to be giving it his all and not merely cashing his check and going through the motions.
The Avengers - Following the blockbuster superhero team-up, the repercussions of that epic adventure are still being felt and not forgotten. Iron Man 3 isn't just an episode that exists in a void as if that previous storyline didn't exist in which Earth was threatened by aliens and saved by those mighty heroes. There are numerous references to "New York" where the climactic battle in Marvel's The Avengers took place, and Tony Stark shows the emotional scars of his experience. One of my favorite lines was when Stark says, "Gods, aliens, other dimensions, I'm just a man in a can." The challenge now with every individual movie that follows (the Thor and Captain America sequels will surely face the same hurdle) is that it's been established that there are a number of larger-than-life characters existing in this shared storyline, so where are they when danger beckons? In Iron Man 3, the President of the United States is kidnapped and threatened, where are the agents of S.H.I.E.L.D. (besides creating a television series for ABC)? Why don't they and the other Avengers team up again to stop these terrorist attacks, especially when Tony Stark's own home is demolished while being broadcast on live TV for all the world to see? Why don't they come to the rescue and why do they leave Iron Man to handle this alone (beyond the fact that this is an Iron Man movie and not another Avengers film)? That was one of the plot holes I wish they had made some attempt to address.
The Mandarin - After highlighting the Iron Monger and Whiplash in the first two films, it was enjoyable to finally see Iron Man's greatest adversary, the Mandarin, front and center. On the flipside, it was terrible how they turned him into a joke. Imagine if they had done something similar to Superman's Lex Luthor or Batman's Joker.
Pepper Potts, Colonel Rhodes, and Happy Hogan - The supporting cast of the Iron Man films is outstanding, and they each had important moments in the spotlight that drove the story forward. The actors involved (Gwyneth Paltrow, Don Cheadle, and Jon Favreau), similar to Downey, are enthusiastic and excellent, serving a story that has some solid scenes even if it all ends up being predictable in the end.
The Armor - As in the comics, the gadgets are part of the attraction as we wait to see what new technology the brilliant mind of Stark has invented. In this particular chapter of the Iron Man franchise, the evolution of the tech is a pivotal part of the tale. I wish we'd had a bit more context and differentiation for some of the armor varieties, for example the Hulkbuster. I imagined Stark, caught up in insomnia and panic attacks, building it in the event that he might have to someday go up against his out-of-control gamma-ray-fueled Avenger friend.
The Kid - Ty Sympkins is fine as the young Harley Keener, and scenes with a child helping a hero are usually an easy way to tug at the emotions of the audience and help children relate to the story, but in this case it didn't fully work. The best use of the cliche is probably Terminator 2: Judgment Day. In Iron Man 3, it felt more like a tacked on scenario, something that might have worked better in director Shane Black's prior action flicks instead.
The Post-Credits Scene - The Marvel motion pictures have become known for adding a little extra after the credits roll. Typically, they've teased future movies -- we've seen the introduction of Nick Fury who laid the groundwork for Avengers, we've seen the first glimpse of Thor's hammer. So the scene here, Stark talking to Dr. Bruce Banner, falls a bit flat. It explains the voice-over narration and it shows that Stark and Banner still keep in touch, but it also seemed a bit trivial. Having Banner nodding off as Stark was allegedly telling him about such a traumatic, life-altering event, seemed to diminish rather than strengthen the bond between the two that I thought was one of the intents of that scene.
There's more of course, but those are just some that come to mind. Let me know what you thought.