This was a great movie for a third installment and a change of directors. Honestly, I liked it a lot more than Iron Man 2. The second one was a fun movie to watch but it was basically just a continuation of the story from the first one with a cooler villain. There was a definite lack of story substance. This movie had a lot more of that and built great off of The Avengers. The continuity that Marvel has created where that timeline is a vital part of this movie and what Tony Stark is going through is awesome. I also liked that they pretty much took him out of the suit for most of this movie. All of the action was still great and there was plenty of Iron Man battle scenes, but it was a great change of pace to see him have to get through stuff without being able to use the suit. As always, Robert Downey Jr's wit/delivery stole the show and this movie was downright hilarious at times. His reaction to a sad boy that he meets in this movie might be one of the out of the blue funniest one liners ever. There was one part of the movie that was equal parts impressive, disappointing and comical all at the same time. I can't go too much into it without ruining it but it has to do with the villain Mandarin. The only knock I can make against this movie would be the partial disappointment regarding that, but it was still very impressively done/marketed and provided some of the huge laughs in the movie.
I would absolutely recommend everyone check this bad boy out. It's another phenomenal entry in the Marvel universe.