Character mistake: When Harley asks Tony what the light is coming from his chest, Tony responds "an electromagnet." Harley replies "What does it power?" An electromagnet is not a source of power. The arc reactor is the power source which powers both the electromagnet (to keep Tony safe from the shrapnel near his heart) and the Iron Man suit. (00:43:25)
Character mistake: Killian tell Pepper the "primary somatosensory cortex" is the pain center. However, this is a gross exaggeration someone of his knowledge would not say. One, the area handles all tactile (touch) receptions. And two, other areas of the brain handle pain, so there's not a "pain center." However, the area that lights up is also wrong, because only the right side would be stimulated since it was his left arm that was touched.
Character mistake: When Happy is in hospital, two bad things happen: One, when a nurse comes into the room, she injects a drug into his IV line, but she doesn't kink the line above where she is injecting, so the drug goes both down and up the line. Two, Happy's IV line isn't attached to a pump. The nurse manually fiddles with the flow rate of Happy's IV. But the fiddling leads to nowhere, as she doesn't look at the chamber where the drops come out - this is very important, as the IV bag can run out anywhere from 30 mins to 3 hours.