Stupidity: Reliant's prefix code is 16309. This code prevents an enemy ship from ordering a friendly ship to lower its shields or something similar. Five digits with no symbols. We know that symbols and letters aren't used since Spock uses a 10 digit set of switches to input the code. This is ludicrous. In 2016, a high powered server could crack a 6 digit password in approximately 0.0224 seconds (at 100 billion guesses/second). Any starship computer would have to far more processing power then a 2016 server. The prefix code protecting a starship from cyber attack would have to be insanely complex in order to be useful.
Plot hole: Why doesn't Reliant know that Khan is exiled here? The Federation is so terrified and opposed to genetic engineering that it's still illegal 300 years after Khan. So why is there no warning along with the data on the Ceti Alpha system? Kirk logged what happened with Khan and his solution of marooning him. Starships use nav data to navigate star systems. Ceti Alpha 6 exploded, yet the helmsman or computer never noticed that there is one less planet than there was when Kirk was there? There is no debris from the explosion? Ceti Alpha 5 is the exact same size and was conveniently blown into the exact same orbit as Ceti Alpha 6 used to have? So there is nothing whatsoever to make the crew even suspect that it's not 6? Enterprise would have to have scanned the planets in the system to know that one was habitable for Khan. Did Ceti Alpha 6's destruction somehow magically turn Ceti Alpha 5 into its exact duplicate? If Starfleet ships have been there to map after Ceti Alpha 6 exploded, none of them bothered to check on the exiles? Pretty callous for Starfleet, don't you think? With the technology and amounts of information available to Starfleet vessels, there is NO logical reason for the Reliant to think that this planet is Ceti Alpha 6. Finally, would the Federation be willing to test a device whose exact effects will be unknown on a planet so close to another inhabited one? (00:21:00)
Trivia: This movie is basically a retelling of another story. When the camera first pans the shelves of the Botany Bay it stops and centers on one book on the shelf in particular.....Moby Dick. That is what this movie is about. Khan is Ahab, The Enterprise is Moby Dick. At one point in the book the whale is circling Ahab's ship on the ocean. At one point in the movie the Enterprise is circling the Reliant (Khan's ship) in the Motara Nebula. Ahab had a scar up one entire side of his body given to him by an encounter with the Whale. At the end of the movie Khan has a burn mark/scar up one side of his body as well. Not to mention that Khan quotes from Moby Dick throughout the movie. The last quote he utters is one that Ahab uttered "From Hell's heart, I stab at thee, for hate's sake I spit my last breath at thee."
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.
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