Continuity mistake: Admiral Marcus' ship "The Vengeance" comes out of warp and immediately appears to be right beside the Enterprise. The top of the ship even goes over the roof of the Enterprise to prove it. Yet from an immediate side angle of the two ships, the distance between the two ships has increased noticeably and the Enterprise is now facing towards the Vengeance.
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.
Continuity mistake: After Harrison (Khan) has attacked the senior officers' meeting and Pike has died, the position of Pike's head on the cushion changes between shots. When Spock disconnects from the mind meld, the stitching on the cushion is above Pike's ears. When Kirk checks for a pulse, the stitching is below Pike's ears. The angle of his head also changes.