Continuity mistake: When John and Emily are in the car at the start, the way John holds the envelope changes between shots. Note the flap. (00:11:20)
Continuity mistake: While Nick and Dana are at the restaurant, in a close-up, Dana lifts the check off the table to show Nick the handwritten phone number; then it cuts to a wide shot and the check is held entirely differently in Dana's hand. (01:27:30)
Continuity mistake: During Brian's jump over the bridge debris, the Ford leans forward pretty far and is still rolling forward by the time the shot cuts. When he touches down, the angle of the car is a lot less steep. (01:28:00)
Continuity mistake: When Admiral Marcus' ship appears in front of the Enterprise after coming out of warp, a set of panels begins to close over the main deflector dish. In the next shot, when looking out of the Enterprise's viewscreen, the deflector dish is fully visible again. (01:13:05)
Suggested correction: This detail was intentional. As a purely military-minded ship, the Vengeance was built with many different defense mechanisms, including the ability to protect its deflector dish by opening and closing a pair of panels. It simply closed them for protection, then opened them again when the deflector dish was needed or the Enterprise was no longer deemed a threat.
The problem is that the doors are shown closing, and then in a split second, when seen from the perspective of the Enterprise, they are still open.
Continuity mistake: Towards the end, right after Mia crawls through the tunnel and into the shed, she backs up against some shelves. There is a lot of blood on her face and her hair is hanging over her face. The shot changes to a close-up and her face now has much less blood on it and the hair that was hanging in her face is gone. (01:16:25)
Continuity mistake: Towards the beginning of the film, Mike is in a diner with a woman. A group of people walk up and they have a conversation. Mike sets down his white cup on the table. This cup continually vanishes and reappears throughout the scene. (00:12:05)
Continuity mistake: After Oz tells Finley he'll get a nice big pile of bananas, Finley tosses down Oz's bag and goes on a rant about monkey stereotypes. When he first throws down the bag, he is close to the middle of the yellow brick road. It cuts to a close up and he is suddenly standing right next to the edge of the road. (00:46:25)