Visible crew/equipment: On the bridge, Uhura tells Kirk that Outpost 4 reported they're under attack, and after Scott says, "I've talked to my engine room, sir. We'll get more speed out of her," we can see the movement of the overhead boom pole's shadow as Kirk walks toward Uhura.
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Other mistake: The red alert light at the entrance to the chapel blinks a few times and stops, even though the rest are still flashing. Also, the last thing Kirk says is "All decks, condition red", which is unnecessary, since the red alert has already begun sounding.
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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 races back into the phaser control room, he places his electronic tablet on the console and kneels to check on the unconscious Styles and Tomlinson. From one shot to the next, the tablet changes its position on the console behind him.