Continuity mistake: When Spock places the viridium patch on Kirk's shoulder, its orientation is horizontal. In the very next scene when Kirk and McCoy beam to the Klingon ship, the patch is vertical.
Continuity mistake: In the fight against the stealth attacking bird of prey near the end the Enterprise gets a torpedo shot through the saucer section leaving a big hole (it's a clear shot through as you can see it blasting from one side to the other) but later when you see the Enterprise and Excelsior attacking the bird of prey the hole is gone and instead you only see burn marks. At the end of the movie the hole is there again
Continuity mistake: In the original UK VHS version of the movie, Scotty beams the Klingons aboard the Enterprise using the controls in the booth (located behind a glass screen). The shot cuts from the booth interior to the Enterprise senior officers awaiting the arrival of the Klingons on the transporter pad - Scotty is suddenly in front of the glass and in the line-up. The shot cuts back to the interior of the booth and Scotty is back in there, operating the controls.