Continuity mistake: 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.
Continuity mistake: 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.
Character mistake: 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.