Factual error: When they are searching for Finney hidden somewhere in the ship, all ship noises are deadened, and the heartbeats of those on the bridge are muffled by McCoy. In order to locate Finney's heartbeat the ship's auditory sensors are magnified by "one to the fourth power". That's 1x1x1x1 = 1, ie no magnification.
Continuity mistake: McCoy uses a "masking device" to block out the bridge personnel's heartbeats. When McCoy masks Spock's heartbeat, he holds the microphone, err, masking device over the wrong part of Spock's anatomy. We'd already established that Spock's heart wasn't in the same place as a human.
Add timeJean G
Continuity mistake: During Kirk and Lt. Shaw's conversation where Kirk learns that Shaw will be the prosecuting attorney, they are sitting at a table. A shot from behind Shaw's left shoulder shows her turning her head toward Kirk. The scene then shifts to a close-up front shot of Shaw, where she again turns her head.