Revealing mistake: When Tony and Rhodes are on the oil tanker bunkered behind an obstacle, Tony realises his gun is empty and asks Rhodes for a new magazine. When Tony ejects the magazine you can see that it is actually an airsoft gun magazine; thus exposing that it is actually a prop gun.
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)
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. (01:30:10)
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. (00:28:45 - 00:29:45)
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. (00:28:50)
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. (01:22:50)
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. (00:56:50 - 00:57:55)
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. (01:30:25)
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. (01:12:50 - 01:14:10)
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. (00:03:45)
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 to 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. (00:51:40)
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. (00:57:55)
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: 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. (01:59:20)