Continuity mistake: When the Thasians restore Yeoman Rand.on the bridge she's barefoot, but when Charlie begs Kirk not to let the Thasians take him because he can't live with them anymore, we see Rand wearing a white fluffy slipper (which she wasn't holding when she reappeared), then she's back to being barefoot again. (00:44:42)
Continuity mistake: Just after the ship is first attacked, Scotty tells McCoy, "We can't fire full phasers with our screens up." Say what? The Enterprise couldn't operate transporters with the shields up, but it fired its phasers, full or otherwise, with the screens up every time it went into battle, and always had. If they'd been forced to shut their shields down every time they fired, the Enterprise would have been history long before this. (00:23:30)
Continuity mistake: At the hearing in the final scene, there are two bits of debris of some sort (small, black and roundish) littering the floor at the bottom left of the screen. Whatever it was disappears when Scott, Spock, Kirk and McCoy get up to leave the room. (00:48:20)
Continuity mistake: After Garth attempts to convince Mr Scott that he is Captain Kirk and to beam him up, while he is banging his fists on the floor in anger he transforms back into himself and the fly like ring on his finger breaks and slides out of shot. It's quite hard to see but it does. The next time we see Garth's hand his ring is intact yet he has not transformed himself again to repair it.
Continuity mistake: When Kirk and Spock are chatting in Kirk's quarters, they finish their discussion and as they head out Kirk orders the ship to red alert. Then after the commercial break, they're on the bridge, the Gorn ship is at a dead halt, and Kirk orders the ship to red alert again. With a hostile ship in the vicinity, Kirk, a highly experienced captain, would hardly have taken the ship off red alert.
Continuity mistake: When Kirk sits down to consult the computer, the big green potted plant on the shelf behind him is there in full shots and missing in close-ups. It's much too large to be completely hidden behind him: if it shows up behind his head in full shot, it should show in close-ups, too, but it doesn't. It's not there. (00:16:30)
Continuity mistake: Spock states that the Fesarius (Balok's ship) "must be a mile in diameter". Yet any one of the small spheres that make up the Fesarius dwarfs the Enterprise. If the Enterprise is about 300m long, the Fesarius would have to be around 6 km in diameter - considerably larger than a mile.