Continuity mistake: In the scene where Thor tells Jane to hold on, she's on Thor's right side and Mjölnir (the hammer) is in his left hand. As they are traveling through the Bifröst to Asgard, the position of each has changed. (00:28:20)
Continuity mistake: When Tony is in his garage injecting his arm, his chest piece is glowing brightly through his shirt, however, the very next shot when he is wiping his arm with the alcohol pad, his chest piece is suddenly turned off. (00:05:15)