(at around 30 mins) When Jarvis and Tony reconstruct the bombing of the Chinese Theatre, Jarvis mentions that, due to the extreme heat of the explosion, everything in a wide radius instantly vaporized. Yet the dog tags of the bomber, while being bent and blued, still have their rubber wrapper.
(at around 29 mins) When Stark is talking to the press and gives out his address to the Mandarin, the image on the reporter's phone is the same as from our point of view, and not what the phone's camera would have seen.
(at around 29 mins) When Tony Stark is giving his address to the press his blue sunglasses are not on when camera cuts to rear shot of his head.
(at around 53 mins) When Brandt comes into the bar, she's seen putting her DHS badge on the table with her right hand in the close up, but with her left hand when the camera cuts away to show her.
(at around 1h 30 mins) When Stark and Rhodes talk to the Vice President from the boat, the Vice President's mobile changes between shots.
(at around 1h 22 mins) When Maya Hansen is threatening to inject herself with Extremis, she says the dosage is 1200cc. That is equal to 1.2 liters, a volume impossible to hold in one syringe.
(at around 8 mins) The story opens with a terrorist attack on Ali Al Salem Air Base, Kuwait, killing the spouses and children of American soldiers at the base. Like almost all U.S. bases in the Middle East, assignments to Ali Al Salem AB are temporary rotations without family members, specifically due to the high risk of terrorism.
Hair lost or burnt off by those injected with Extremis grows back along with missing body parts. While hair is living within the follicle, once it's outside the skin, it's dead and cannot be regenerated in its current state. (As long as the follicle is not damaged, it can be regrown, but styling would not regenerate.)
(at around 1h 5 mins) Tony instructs Gary to "jump on the roof, recalibrate the ISDNs, and pump it up by about forty percent." What Gary adjusts is a satellite dish, whereas ISDN connections are hardwired using the same telephone system that is used for what is no known as a "landline." Even if it were an ISDN connection, Dual ISDN PRI has a max downstream bandwidth of 2.94Mbps, but the speed test shows a speed of over 9Mbps. Neither ISDN nor Satellite Connections could be increased in speed by simply making adjustments to the receiving equipment, with the possible exception of repointing the dish to a different satellite, which would be done using the equipment inside the van. Additionally, the screen shows two different IP addresses displayed in the standard system of four numbers, but one of the numbers in the first address and two of the numbers in the second address are above 255, which is the upper limit of number in actual IP addresses.
Tony dumps cooking oil on the floor and then lights it, as if it's kerosene. Even in an alternate reality, no one would cook with an oil light enough to evaporate & burn that easily - especially in a kitchen that uses gas-flame equipment as shown. The kitchen would catch fire every time that oil was used.
(at around 1h 41 mins) When Tony and Rhodey are at the docks and taking cover, Tony asks for more ammo for his pistol, even though Rhodey tells him all bullets are not interchangeable. Tony acknowledges the irony of him being an arms dealer: "I know what I'm doing, I make this stuff. Just give it to me."
(at around 1h 30 mins) While Tony and Rhodey are talking to the Mandarin before getting onto the speedboat, the injuries to Tony's left eye are shown on his right eye instead.
In the final shot, the sound of an internal combustion engine was added to the visual of Stark driving off in an electric car.
When he has Jarvis pull up the 3000 degree spots not designated as the Mandarin, the one in Rose Hill shows it to be in the NW corner of Tennessee, Thus, when he goes there, he should not drive past the Miss Chattanooga Pageant (south central Tennessee and 100's of miles away).
While the Extremis Soldiers can heat up metal to near liquid states, their clothing remains completely unaffected.
Tony reiterates that the suit is powered by electricity, because he has to keep re-charging it externally. But in the first film, it's established that the suit is powered by the arc reactor in his chest. So it should have full power every time he gets into it.
In Iron Man 2 (2010) It's established that Tony Stark has security precautions in place that prevent unauthorized people using the War Machine suit. However in this movie one of the Extremis can use it without any trouble.
Tony taunts the guards by counting down to the arrival of his suit, and eventually, the left hand and right foot arrive. Then the scene cuts to the locked barn door that the suit is trying to break through, as if there's not already a hole somewhere big enough for the first 2 pieces to have already exited.
The Mark 42 suit pieces are shown flying across the house in a few seconds during the house attack scene. At that speed, it would take days for them to fly across the continent in the dungeon scene, but they still arrive in seconds.
When Tony and Rhody are in the restaurant, Tony said "Einstein slept three hours a year. Look what he did." While this is most likely a joke, Albert Einstein actually slept, regularly, 10 hours a night. This, along with daily naps, he slept more than the average person.
The President salutes when the Iron Patriot arrives. The latter is the subordinate and should salute first.
(at around 1h 35 mins) Radical differences between altitudes when Iron Man is saving the airline passengers. At one point Jarvis calls out "18,000" feet and then only eight seconds later he calls out "10,000" feet. Nothing falls at 682 miles per hour from natural gravity. Then Jarvis calls out the last 9,400 feet in twenty seconds, nearly three times longer than it took the first distance.
Harley suggests that the Iron Man suit could be improved with "retroreflective" panels. But retroflectivity merely returns light to its source, like road signs, road markers, vehicle reflectors, and red-eye in flash photographs. Retroreflective panels would make the suit easier to see when a light is shone on it - not camouflage it.
(at around 1hr 27mins) When Harley releases the Iron Man suit from his garage he is wearing a Science Club top where his name is miss-spelled as "Harley Kenner"