Overall of the science or pseudo science of the movie:
The science of IM3 is disjointed, while IM1, IM2 and Avengers touch one particular notion of science (mainly physics and mechanics) and expand on it, IM3's sciences tries to connect all these branches of science namely genetics (plant and human), nanotech (not specific), neurology (related to genetics, but in this case: brain structure), physics (energy/heat) without any logical linkage.

While you may use the Extremist (take the essence) story-line, you can ground it with logical (current) science. If large liberties are taken with the Mandarin, why not "ground" the Science as well.

Biology
1. Lost limbs are healed quickly, fine (as ridiculous as a nameless mutant on X-Men3 or Amazing Spiderman's cicak), why does scarring on the face of Brandt still remains.
2. Changing of DNA, that enables A) Regeneration of body parts. B) Produce heat and C) Survice the heat generated beyond any living lifeforms. Whatever protective protein that an organism can generate is still based on organic compounds that are not able to withstand heat able to melt metal. Too many functions of convenience. Extremis comics I believe did not go to such "extreme", human bomb and heat.
3. While vetebrates have a neurosystem, plants do not, lets just say the relation in which both are essentially bombs are due to DNA. Which bring to a point: slot's in the brain does not keep the blue-print, but your Genomic DNA does. Why the brain relation (apart from the excuse of hologram for Killian and Potts). Black and Pierce essentially took what's wrong with Extremis virus notion, throw out what's logical and incorporated new stuff that's illogical.
4. Healing of bullet holes on the extremis soldier, sure the flesh heals but the fabric don't.


My Nic-picks, less on science, more on story
1. While Mk. 1-6 are powered by the ArcReactor, Mk. 7 of Avengers might be. All other Mark's appears to have self-container power sources. Mk.42 however appears to run on rechargeble batteries. As genius as Tony is why does he not have to foresight to utilise the power on his chest, and rely on what appears to be charged by power-mains from the garage or boat. Fine, it's a prototype excuse.
2. IM3 is almost all on the Man, little to no emphasis on the armors except for just a little on Mk.42. No cools hologram on design of armors.
3. Other than Mk. 42, I believe Tony put on maybe only 3 or 4 other armors. There rest are mostly just eye candy and fireworks.
4. IM, IM2, Avengers all kept the legacy of previous armors, shows a continuity. Starting all from a clean slate after IM3 kind of reduce the significants of all previous movies. Why thrown the triangle reactor, it's his, his father and Vanko's legacy, big plot points of IM2 and Avengers.

What's good
Action sequences showing Tony's "kung-fu" with the armor and partial armor.

Banner and Tony ... minor banter

Just glowing skin and eyes....

Starting from Mk. VII (7) in Avengers, the suits no longer needs to power from Tony's chest.

Mk. 42 is even worst, it apparently runs on rechargeable batteries, it cannot even utilize Tony's ArcReactor when it ran out power, needing charge from power grid or from boat. As great a genius Tony is, he should have know-how to charge his suit with his ArcReactor....

All other suits including Mk. 7 are self-powered, presumed with it's own ArcReactor(s), except for Mk. 42.