Problems:
The Mandarin... just dumb. For a major villain of the comics, treating him in that way was just terrible. It was like a slap in the face of all the fans of the source material. I read so many reviews that said Ben Kingsley was a huge reason to see this movie, until he was turned into a joke of a character... yeah he did well.

Joke after joke after joke after joke. I couldn't even finish laughing off the first joke before they threw another in. It felt very Michael Bayish, just forced humor around huge special effects the only thing it was missing was the racism.

Not believable, even for a comic book movie. When you issue this complaint people say, it's a comic book movie!!! At least the first Iron Man strayed more towards believable and an actual plot. How did Pepper become a badass, where she could roundhouse kick an explosive at a bad guy and then simultaneously shoot it with the hand cannon while it was in midair just before it hit the target? Honestly the coolest part of the whole movie was when he forced the Mark 42 armor onto Killian to blow him up. That alone would've been an awesome way to kill the big baddy. If one explosion didn't kill him then how the hell did Pepper's explosion to the face do it? Trust me, throw the Mark 42 armor on Killian, blow him up, have Pepper show she's alive, then do the ending.
Do you really believe that he could link 13 people together in midair as they're plummeting to the ground? Also a missile from a helicopter flies into the house and explodes right next to them and all that happens is they just get knocked back? Really? No ringing in the ears... just some scratches. The whole thing felt like they said throw it all out the door because this movie is about humor and special effects.

Extremis. Just a forced plot that had so many holes the experiment should've been called Prometheus. Extremis was developed as a way to heal people's injuries. How the hell does it allow the person to essentially melt inside, breathe fire, and have super strength to knock Iron Man around? In no part of the movie did they explain it really. The just said that it works sometimes and other times it causes the person to explode and become a human bomb. If you were going to go completely unbelievable, go with the Mandarin and the 10 rings. If you were going to go down that road, utilize your special effects and focus on Kingsley as the primary antagonist with super powers, like we all thought the movie was going to be about. Say the ten rings were the result of The Avengers movie plot, if you're going to go that way don't completely mislead your audience just to shift gears midway through the movie. Ask Spiderman 3 about having too many villains.

The middle of the movie. Boring. After his mansion gets blown up he wanders around for a good 30-45 minutes without Iron Man even being in the film. Even Rhodes was out of his War Machine/Iron Patriot armor for way too long. They took the Iron Man out of Iron Man. Also what was with that woman grabbing Iron Patriot on the wrist and melting him a bit and he just falls over. Same happened to Iron Man at the end with Killian. Is the off switch to the suit located on the wrist?