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)
Continuity mistake: When Jordan is inside his Mercedes trying to escape with his daughter, his wife breaks the door glass and the shot changes abruptly. When she breaks the windows Jordan doesn't have a ring, but when the shot changes the ring appears on his finger again. (02:43:30)
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: When the two criminals seen at the beginning kill the drug dealer, he is initially still sporting his sunglasses, rolled at the back of his neck. When they drive away, the shades somehow ended up in a totally different spot around his midsection. (00:03:55)
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.