I'm late the hype forums but you can summarize my beef(s) with IM3 as this: it took everything good from the original comic concepts or storylines and dumbed them down.
The Mandarin: an extremely powerful villain for Iron Man, one of the few who challenged Iron Man's skillset with the ten rings. Admittedly a difficult concept to translate to film, "ten magic rings." My response? Instead of dumbing his abilities down, just don't use him. His Silver Age origins made him a dull character, but in recent decades he developed a more interesting motivation in the comics, one that was evil yet had a perverted humanist perspective, instead of maniacal greed, hatred, or revenge. Again, just don't use him if you can't use the best of the character.
AIM: Like Mandarin, AIM started out in the Silver Age as a typical Silver Age bad guy organization, but in time, different Marvel writers fleshed out the ideology of AIM. Science over all. Radical experimentation to make a better world. The ends of scientific utopia justify the harsh means. Such a terrorist organization has a (fairly) unique voice, at least in the MCU. The film adaptation? I'm still not sure what AIM stood for...controlling the War on Terror, I guess? Again, the best about AIM from the source material gutted, with hardly any resemblance on screen. You could have called them Roxxon Oil and it wouldn't have made any difference on the plot or behavior of the characters. Killian could have been an interesting villain, someone pushing for advances in humanity from an ethical perspective, just not factoring the consequences. Someone who believed superhumanity would eradicate the flaws of humanity, and the Extremis virus was the means to that improvement in the human condition. The film muddled this with nerdy Syndrome/Edward Nigma parallels instead of embracing the gray area and tension (that makes good storytelling) that could have been created if Killian was an ideologue in the Age of Miracles.
The film adaptation seemed to be a not-so-subversive allusion to "Loose Change" beliefs that what's wrong with the world is some defense contractor manipulating things behind the scenes, and there can't possibly be any evil other than this. IM1 and IM3 had the same villain--Stane manipulating the Ten Rings...Killian manipulating the Ten Rings. IM2 wasn't far off--Hammer manipulating (and being manipulated by) Whiplash. Oh, and Loki manipulating the Frost Giants and Hydra SHIELD in CWS (obviously they'd done pretty well with Loki comparatively, but the IM villains haven't had any of that pathos developed). Yawn. One of the things that made Marvel so great, particularly in contrast to DC, creating so many fans for decades, was not just the humanity of its heroes, but the humanity of its villains. Dr. Doom wants to conquer the world as much to save it as to feed his ego. Magneto wants to save his people. Even Thanos does what he does out of love. What makes a great villain is the kernel of "good" in him that gets twisted, perverted, or corrupted when taken to the extreme or misapplied in the wrong context. Every good villain has a good cause behind him. Marvel Studios has instead adopted the DC Silver Age approach to villains, dullards with simplistic motives, through this addiction to misdirection "twists." These waste screen time and results in a bland Third Act caricature, instead of just playing the antagonist straight, with a personality, soul, and conflicted program for making the world a better place or fighting injustice.
Iron Man and Extremis: These go hand in hand. The Extremis story would have been nothing, not even a drop in the pond of Marvel, if Iron Man doesn't adopt and adapt the virus himself. The best part of the Extremis storyline was Extremis Iron Man. It flipped the narrative of Iron Man from being dependent on technology to even live to superceding human limitations. The lukewarm end of IM3--where he was no longer dependent on the armor to live, nor the summation of human perfection (and beyond) via Extremis--was absolutely the most boring, un-Iron Man approach to the character. Tony Stark should be either dependent on technology or superhumanly enhanced by it...cause he's Iron Man. The action sequences likewise missed the point as well, as most fans of Iron Man want to see Iron Man in action, not Tony Stark. In the MCU, Joss Whedon has done the best in portraying Iron Man in action in limited screen time of one film--flying and using repulsor rays at once--then all three IM films combined.
