Continuity mistake: Joe is looking through his yearbook while Marie chats with the old headmistress. He finds the page with Adrian's photo. At first, the name under the photo is Adrian Pryce. In the closeup shot, it now reads Adrian Doyle Pryce. (01:12:20)
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 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)