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: When we first see Conti, there is a shot of a man shaving and the blade is up past his ear. As the shot changes, the blade is now under his ear. (00:06:00)
Continuity mistake: When Oscar is on the phone to learn about the location of the job interview in the warehouse district, the paper that was on top of the payphone jumps suddenly in the hand that holds the receiver to his ear, with the phone call already being over. (00:22:25)
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)