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.
Factual error: During the Vengeance's fall to Earth, just after hitting Alcatraz, the saucer section hits the surface of San Francisco Bay, the outer rim diving dozens of meters into the water and its rear lifting up almost vertically into the air. A few seconds later the ship is seen from the onshore view, and it is straight and level and heading directly at Star Fleet Headquarters. Hitting the water at that angle and speed, so close to the shore, the ship could not have righted itself and gotten on that trajectory going that fast. It should have sunk or flipped over when it hit the water. Even if it could flip 360°, there was not enough time, distance, or height for the ship to continue on to its target at that speed. The water's drag would have slowed it too much. (01:52:40)
Suggested correction: Maybe the ship's systems are trying to correct its course.