Continuity mistake: After Tony gets the armor back at the Mandarin's hideout and meets up with Rhodes, they go by boat to the harbor. On the way Tony calls the Vice President - during this scene the VP's phone changes, note the camera on the back of the phone is visible, but in another shot right after, it is a completely flat back panel.
Continuity mistake: Tony is in the bedroom with Maya Hansen, Happy is seen closing the sliding door. With the door just inches from being fully closed, a quick cut to Tony and Maya kissing, then back to Happy, and the door is almost fully open, with Happy in the process of closing it again just as the plant explodes.
Other mistake: When Tony's house is destroyed by the Mandarin, watch closely when Pepper is blown through the air, just before Tony attaches his suit to her - she's very obviously wearing high-heeled shoes that would make it impossible for her feet/ankles to fit correctly into the suit without them being crunched up by the suit's boots. But later on, when she gets out, if you listen, you can hear the "clicking" of her unbroken heels as she runs around.
Factual error: When Maya is trying to get Killian to let Tony go, she holds a dose of Extremis to her neck and says "1200 cc's - A dose half this size, I'm dead." 1200 cc's is 1.2 litres, or over 40 oz/2 pints. What she's holding is barely the size of a cell phone, nowhere near that volume.
Plot hole: How come the Extremis serum was able to regenerate Ellen Brandt's arm but not repair the scar on her face? According to the movie, the serum is supposed rewrite the body's genetic code and constantly repair damaged cells, so her face should have been restored to its original state, just like her missing arm. Even if she had been born with the scar the serum would have healed it, just like it healed all of Aldrich Killian's physical impairments.
Continuity mistake: When the Mark 42 is "done" assembling for the first time, in Tony's workshop, a digital model of the suit appears in the lower right corner of the screen. In this render, the suit is complete, but a moment later there is still one piece missing, which hits Tony so hard the entire suit falls apart.
Continuity mistake: When Tony is creating his weapons, one shot shows the electric glove he is wearing to be designed for his left hand. Later on, when he is in the Mandarin's mansion, he attacks one of the guards with the electric glove, only now the glove is on his right hand.
Factual error: In the scene in Tennessee, when Tony is being chased by the glowing "homeland security" lady. He throws a jug of oil and lights it on fire with the red hot handcuffs that he takes off. Then he somehow manages to slip a set of dog tags in a microwave and turns it on. This is to create a spark to explode the gas line that he pulls from the wall, which somehow isn't ignited by the large grease fire in the same room.
Continuity mistake: When Tony and Pepper are attacked by 3 missile-wielding helicopters, Tony, dressed in his metallic suit, has blood on his nose and cheeks. Problem is: The blood increases on his face, which is normal as it is still bleeding, but then it lessens. Then it gets worse again.
Continuity mistake: When Tony is attacked by helicopters in his Malibu mansion, his right hand has a black wrap around it. After he gets buried by rubble underwater in the suit, his right armored hand detaches and grabs his bare right hand to pull Tony out from the rubble. Tony's bare hand no longer has a black wrap.
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.
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.
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.
Continuity mistake: When Tony and Rhodey first get noticed as they search the oil platform, one of the Extremis soldiers starts shooting at them. They dodge the bullets and hide. Tony then says "You see that? Nailed it" and he is shown to be looking at Rhodey. Next shot, he's suddenly looking downwards.
Other mistake: Immediately before the helicopter attack on Tony's house, Maya (the "botanist") looks at the TV set, which shows a news chopper shot of the home, and says "Should we be worried about this?" It's only a moment later, when everyone looks at the screen, that a missile track appears on the screen.
Continuity mistake: As Maya is showing Tony her research, in the shot where Tony says "Essentially, you're hacking into that of the genetic operating system...", Tony is shown to be looking at Maya. Then as he finishes off the sentence with "of a living organism" in the following shot, Tony is suddenly looking at the computer.
Continuity mistake: When Tony tells Killian to go to the roof, he leaves the lift. In this shot, there is a strand of Killian's hair layed over his face and nose in a straight line. In the next shot as he says "I'll see you up there", the bottom of the strand is suddenly curved over to the left side of his face.
Continuity mistake: After Tony hangs up on Happy using Face-Time, the scene cuts to Pepper and Killian having a conversation. As Pepper says "As in, enhanced soldiers, private armies, and Tony is...", she is cut off by Killian. When Killian starts speaking, he shifts his head to the left and starts looking downwards. In the next shot, he is suddenly looking straight back up at Pepper.
Continuity mistake: In 1999, when everyone exits the lift, Tony and Killian stay inside the lift. As everyone leaves, Tony places his hand on the door frame. In the following close-ups of Tony and Killian, Tony's arm never shows any signs of moving his hand, but as he leaves the lift, his hand is no longer on the door frame.