Continuity mistake: While Kirk and McCoy attack the other two henchmen, Spock shoulder-pinches the card-playing gangster. In the very next shot, Spock's position has jumped from behind the now-unconscious man to several feet away, where he is bending over to retrieve the guns from the floor.
Continuity mistake: In the very first scene after the intro, when Bela's goons hold the landing party at gunpoint, Spock's position on the sidewalk shifts back and forth from standing on the other side of a wooden bench to standing alongside Kirk and McCoy with no bench in between. In fact, in the latter shots, the bench has moved all the way across the street.
Continuity mistake: The scene outside shows a guard standing close to a sign on the wall that says, "Jo Jo Krako", but the next overhead shot shows the guard further away, and a railing between the sign and the guard that would have prevented anyone from getting close to it.