Corrected entry: In the scene at the crater when Thor breaks in and then is fighting the giant SHIELD guard, the fight ends up outside, and it is pouring rain. Thor and the guard are both soaking wet during the entire fight. However, when the camera cuts to shots of Hawkeye, who is watching the fight from an open platform above them, Hawkeye is completely dry. The scene shows him out in the open with no covering and there are several clear shots of Hawkeye's face, but there is not a single drop of water on him.
Corrected entry: At the end when Loki goes to lock the Bifrost on Jotunheim, he's carrying Odin's staff and wearing a helmet. He slides the staff into the machinery to open the Bifrost then freezes the electrical streams (with the staff in the middle of it) and his helmet is gone. Thor comes in to stop him and he's got the staff back from inside the ice and his helmet is back.