Factual error: Shortly before the EMP bomb is activated, the crate containing it is shown. "Diese Seite Oben" is painted on the box, which is a bad translation of "This side up." In Germany crates only use the word "oben" to indicate the upper side of a box.
Continuity mistake: At the end of the film when they are fighting in the chambers, Captain America destroys the right boot thruster. Later, they say it is the left, and the right one is fine. (02:04:15 - 02:05:30)
Continuity mistake: Near the end of the movie, Rhodes' face is sweaty when he's sitting on the floor of the compound; but when Tony helps him up, the sweat is gone without Rhodes wiping his face.
Suggested correction: He has a light glisten to his face. It reflects harder on the floor than when he rises (more sunlight). But, it's still the same.
Continuity mistake: In the opening sequence, the courtyard outside the lab is filled with bodies. Scarlet Witch pulls the gas out of the building and sends it into the sky. We then get a wide shot of the gas and in it the courtyard is completely empty of bodies, including Wanda and Falcon. (00:07:18)
Continuity mistake: While the sink is filling in the interrogation scene, the water is running over his shoulder, however when the camera shifts above, the faucet is not close enough to have water running over him. (00:25:00 - 00:27:00)
Continuity mistake: The end of the movie shows the jailed Avengers with their wounds still visible, while the others at the Avengers compound are mostly healed, including Rhodes.