When Pepper is watching the television program about Stark Industries' stock troubles, after Tony's press conference, notice she has a wireless headset in her left ear. When Tony calls her down to the lab, the camera flashes back to Pepper and the ear piece is gone.
When we first see Tony Stark arrive at the benefit, his car doesn't have a front plate. When we actually see him pull up to the entrance though, his personalised "Stark" plate has appeared.
In the shot just before Obidiah paralyzes the guy that held Tony prisoner, the ear plugs are not in his ears and when he paralyzes him they are.
In the montage of Stark designing the Mark II suit on his computer, he picks up a coffee mug to his left and absent-mindedly drinks it, then gets a not-good expression as the liquid was presumably not what he was expecting. A second earlier, the coffee mug had been shown completely upside-down on the desk.
There is a misspelling on the cover of the issue of Forbes magazine shown in the presentation about Stark's life. It reads "Tony Stark takes reigns at 21". The correct spelling of the word is "reins". Stark may "reign" at Stark Industries but he would take over the "reins" of the company.
When Ivan is first brought to meet Hammer, Hammer is eating a dessert with a cherry on it. The cherry disappears and then reappears. The spoon also keeps swapping between being inside the food and by the saucer.
In the opening senate scene, the Senator's jug of water keeps turning around and moving closer/away from the nameplate between shots.
When Mickey Rourke puts the explosive onto the wall, he slaps it down and it spreads out a bit. We cut to a quick closer shot, and it's suddenly more compacted.
When Ivan climbs the ladder to inspect the Hammer prototype, his hair changes repeatedly from underneath the frames of his glasses to outside the frames.
In the scene where Whiplash talking on the phone with Tony, you can see fresh blood running down his hand, but when it goes to the close up of him, the blood is wiped off and there is only a stain.