Question: Even though it's meant as a comedic moment, I've never really understood why Kirk would be so nervous about Saavik piloting the ship out of space dock. She's not actually flying the ship, so it's not like she's going to crash it into the wall or something. Plus, Sulu is an experienced pilot, so even if she said something stupid like "Warp speed!", he's unlikely to follow the order. Just something odd that I have always wondered about.
Question: This isn't technically a mistake per se, but it involves Spock's funeral. Several Enterprise crewmembers are killed during the battle with Khan, and yet only Spock gets a funeral. Perhaps there was a smaller memorial for the others, and Spock got a full funeral due to his status as captain, but why is Kirk only sending Spock's body to the Genesis planet? I imagine he sent only Spocks's body there since in ST3 there aren't dozens of little regenerated human babies crawling around down there.
Question: After the Reliant ambushes the Enterprise, Kirk tricks Khan and hammers the Reliant into retreat. As Kirk turns to assess damage to the Enterprise, Scotty inexplicably appears on the bridge, carrying the charred body of Midshipman Peter Preston. Why on earth would Scotty bring the dying Preston to the bridge, rather than to SickBay with all the other injured? He had to deliberately bypass SickBay just to make an unnecessary appearance on the bridge.
Question: This always kind of bugged me. Why would David think that Kirk murdered everyone left behind on Regula One? Even though they did not have a father/son relationship, surely the heroic exploits of James T. Kirk are well known? At one point, David even refers to him as an "overgrown Boy Scout." I've seen this movie a hundred times, but could there be something I'm missing?
Question: When the Enterprise recovers Chekov and Captain Terrell, they just accept Chekov's and Terrell's false explanation, even though McCoy is standing right there with a medical tricorder. Why didn't McCoy's medical tricorder pick up the Ceti eels lodged in the brains of Chekov and Captain Terrell?
Question: Where would Kahn learn a Klingon proverb? He was marooned on a planet, and before that he was in hibernation.