Continuity mistake: As Decker is talking about the Planet Killer, the camera looks at McCoy. His left eyebrow is slightly arched, and his hair is styled differently. It can be seen that this shot is reversed from normal.
Audio problem: About a minute or two into the episode, Captain Kirk says "That's incredible" but his mouth doesn't match the words.
Continuity mistake: In most shots, the Constellation's impulse engines are lit up orange, but when moving to meet the Enterprise, they're not lit up, though the ship is moving.
Continuity mistake: Spock nears the command chair, where a seated Decker is leaning on the left armrest. A second later he is leaning to the right.
Continuity mistake: First, Scotty rigged a self destruct delay timer for Kirk that supposedly had thirty seconds programmed in. However, putting a timer against the one used in the episode, from start to finish there was one minute twenty seconds before the Constellation blew up. Second, Kirk was holding the communicator out and away from himself before his beaming, then it's close to his face as he materializes. (00:47:05)
Continuity mistake: Decker is leaning over the forward console between Sulu and the other man, with Spock at his left elbow. As he gives the order to veer off, he starts to turn to his right. As the angle changes, it appears that he was standing straight up the whole time.
Visible crew/equipment: On the Constellation, the camera is looking at the man helping Kirk to get the secondary view screen working. As the camera goes to pull back to allow Kirk into the shot, you can see the shadows of the camera shades on the wall. (00:25:00)
Revealing mistake: While Kirk watches, the machine fires at the Enterprise. As Spock is knocked backwards, watch his hands as he goes forward. They automatically go into a certain, almost practiced position. Then a moment later, the Communications officer is reporting to Spock. As she does, another shot hits the ship. She and just about all the crew react to the jolt a second before the camera and lighting crews simulate the hit. (00:26:40)
Revealing mistake: Accounting for some effects being re-done by modern digital formatting, when the Enterprise approaches the drifting Constellation, as it rotates, you can see a star pass through the solid part of the Constellation's saucer.
Other mistake: When the Planet Killer hits the Enterprise, the ship lurches 45° to starboard, and the crew fall accordingly. However, the chairs, except for the communications station, stay in place.
Plot hole: Commodore Decker takes over command of the enterprise but Spock says if McCoy can certify him incompetent (which he obviously is) he can be relieved of command. McCoy says he will certify him now, so why doesn't he? In other episodes it has been stated that McCoy can order anybody regardless of rank to an examination to see if they are physically or mentally fit.