Other mistake: When talking to Edith Keeler one evening, Kirk refers to a star in Orion's belt, pointing it out. The shot then cuts to a scene of the horizon. The sky is quite cloudy and the light from the sun is still lighting the horizon. The stars would not be visible.
Revealing mistake: Chekov covers Mara's mouth with his hand when he assaults her in the corridor. Kirk intervenes and throws Chekov against the opposite wall. Brown streaks form where Chekov's hands hit the wall, most likely from the brown makeup used to create Mara's skin tone.
Continuity mistake: When Kirk, Bones, Chekov, and Spock go over to the Defiant, the suits they have on have a black support bar in the left side of the headpiece. When the camera looks down at the dead men and back to Kirk, you see the bar is on the right, and his hair is parted on the right. The very next look at Kirk, the bar and the part of his hair is back on the left.
Plot hole: Because of the magnetic ore on the work clothes of the man who beamed up, the transporter made duplicates of everything put through it, and so couldn't be used. This was further complicated by the control and power circuits being blasted by the "evil" Kirk. However, the ship carries a number of shuttle craft, which no-one mentions.
Continuity mistake: In Janice Rand's quarters, Charlie mentally throws Kirk and Spock against the wall. After they collide with it and slide down the face of the wall, there is a huge indention and crack where Spock hit. After a camera cut to Charlie, when the camera looks at Kirk and Spock again, there is no damage to the wall.
Continuity mistake: After Sam tossed Kirk, he goes to a bench in the corner, picks up the towel that was there, and sits down. After Kirk tosses Charlie, Sam is laughing, and Charlie makes Sam "go away." After Sam fades out, the towel that he had around his neck is lying there, when it disappeared with Sam.
Continuity mistake: Midway through the episode, a stock shot of the view screen shows Sulu at the helm. When we return to the bridge master shot, however, Sulu isn't there. Styles is the only one at the console, and he's sitting at navigation. The helmsman's chair is empty.
Continuity mistake: When Spock goes outside to scan the area he looks at the building directly in front of him, but when the child rubs away the dirt on the window Spock is seen looking at the ground to his right. But in the next shot Spock is looking directly at the building again.