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)
Character mistake: When Steve is at the Smithsonian, he reads the biography of his friend Bucky. At the start of the description, the bio reads "Born in 1916...", but at the bottom of the description, it reads "Bucky Barnes: 1917 - 1944." (00:18:35)
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.
Character mistake: Thor calls Nidavellir "Nivadellir" the first two times he mentions it.
Character mistake: When they infiltrate the military facility, Steve and Tony are trying to blend in. Steve wears his hat the entire time he's indoors. He's a soldier, taking his hat off when he comes through the door would be second nature to him. Not removing it would make him stand out as someone who doesn't belong - Steve knows better than that.
Character mistake: Dr. Erskine says he lives in Queens at 73rd Street and Utopia Parkway. Actually, 73rd Street is well to the west of Utopia Parkway (both run north-south). Erskine must have meant 73rd Avenue, which does cross Utopia Parkway.