Continuity: The blood stain on Kirk's jacket keeps moving around.

Continuity: When Khan's number one officer is dying in the arms of Khan, they exchange a word or two before the first officer dies quite dramatically with his eyes open. Khan then fully embraces the corpse and looks up to the viewer screen and vows to get even with Kirk. However, the "corpse", whose eyes are open, closes them upon Khan's embrace.

Revealing: When the Enterprise first encounters the Reliant, we see several screen shots of the Reliant on the Enterprise viewscreen, and several shots of the Enterprise on Reliant's viewscreen. The puzzling thing is, if you watch very closely to the shots of the Enterprise on the Reliant's viewscreen, you will notice that the stars are actually moving BACKWARD, as if the Reliant were in a slow reverse. Obviously this is an editing blooper since Khan just ordered that the ship slow to one half impulse power, which still moves the ship forward.