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: When Stark gets trapped by the water tank he is completely soaked. When he walks back to the car with the boy he is completely dry and his hair is restyled with not enough time for this to happen.
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.
Factual error: At the end Tony drives an Audi R-8 e-tron, which is an electric car, and while it has a sound system to produce an artificial engine noise, it doesn't sound like what is heard.
Factual error: When the Iron Patriot armor is shot at on Air Force One, the bullets ricochet and smash a window. The windows on Air Force One are bulletproof.
Continuity mistake: Before Tony sends a holiday greeting to the Mandarin his car is pointed one way when he gets in, then the car faces the other direction.
Continuity mistake: When Tony is giving his address to the Mandarin through the media the reporter in front of him has a cell phone which changes design between shots.
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: 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.
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 and Rhodes leave the Mandarin's mansion, Tony has blood on his left eye and cheek, which changes to the other eye between shots, then changes again at the boat.