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)
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. (01:32:55)
Continuity mistake: When Ellen Brandt is confronting the Police Chief of Rose Hill, TN at the bar. The weapon that is visible that Brandt takes is a semi-automatic with a single stack magazine. The weapon which she shoots has a double stack magazine. (00:54:10)
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)
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: 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: 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)
Continuity mistake: When Tony Stark and Col. Rhodes confront the Mandarin in his chair the hammer for the Beretta is forward after Rhodes loaded a new magazine. The hammer is shown in the back position in a subsequent shot. It happens twice during this scene. (01:30:05)
Continuity mistake: When Tony is sending a holiday greeting to The Mandarin, he has sunglasses on. Then in the shot from behind, he doesn't have any glasses on. Then they reappear in the next shot and then he takes off the sunglasses. (00:28:55)
Continuity mistake: When Tony is in his garage injecting his arm, his chest piece is glowing brightly through his shirt, however, the very next shot when he is wiping his arm with the alcohol pad, his chest piece is suddenly turned off. (00:05:15)
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)
Continuity mistake: When Tony is working on the laptop in the van, the IP address shows as 934.554.32.3. Not only is that an invalid address, but when he enters Rhodes' credentials, the IP changes to 93.455.43.232 (also invalid). (01:05:45)
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)
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)
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)
Continuity mistake: When Jarvis wakes Tony up when he is in Tennessee, there is quite a lot of blood on his face. But when he takes off his mask, so before he had any time to wipe it off, the amount of blood decreases significantly. (00:39:50 - 00:40:30)
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.
Chosen answer: The Battle of New York was never specified to take place in 2012, we just know that the film came out then. Based on the newspaper we can assume that the battle was in June 2013, rather than some time in 2012 as many would have previously assumed.