DS9Sega covered most of the really glaring plot holes, but there is one other thing that I don't think has been mentioned yet that just makes me tear my hair out. During the first encounter with the Reliant, what the hell is with Kirk just refusing to put up the shields??
That one bugs me too. There's just no logic to it. It they were making first contact with an alien species, or approaching something like V'Ger, and Kirk wanted to avoid appearing aggressive or something like that, I could understand his hesitation at raising shields. But in this case, we're talking about a Federation starship. If nothing's wrong and it's just a simple hardware failure blocking communications, Reliant's captain is going to understand why Kirk raised shields. He's not gonna suddenly start firing. And if anything is wrong, you've taken the proper precautions. Those shields should have been up from the moment Kirk observed "This is damn peculiar."
In addition, if we cut him some slack on that, there are two occasions when it becomes crystal clear that something bad is about to happen. First, the Reliant sends a message explaining the reason for the lack of communications. Spock confirms that message is false. Red flag number one. Second, Reliant raises her own shields. Big, glaring red flag number two. That Kirk ignores both of those events and waits until weapons are locked onto his ship to raise shields goes beyond bad judgement and into just plain incompetence.
Because if they had some old charts of the system and were specifically looking for the sixth planet & its orbit----they still would have gone to the trouble of locating all the other planets in the system before beaming down to the planet currently in the orbit of the sixth planet.
Sarcasm aside, I get what you're saying, but we're not talking about a sailing ship with a paper map. We're talking about a starship with 23rd century sensors and an advanced computer system. As they approached the system, the computer should have alerted someone -- the science officer, the navigator, anyone -- that a system which is supposed to have six planets now has only five. The idea that an entire planet being missing form a system went unnoticed by the science officer, the navigator, the helmsman, and the ship's computer is ludicrous at best. And even if we grant that, Khan states that Ceti Alpha VI exploded six months after they were left there. Which means it's been gone for almost fifteen years. And in that time, not a single sensor probe, monitoring station, or starship has noticed either the huge explosion in the Ceti Alpha system or the absence of one of its planets? Not a chance.
*What was Spock really doing in the Radiation chamber? Suddenly, the ship can't go to warp, so he runs down there, sticks his hands in the upside down fishbowl, and suddenly all is good. Did he give it a mind meld? If it was a persistent problem from the first attack, why didn't they send guys in there with radiation suits on and fix the problem normally? If you know you're going into battle, having the ability to escape should be priority one.
Mr. Scott's Guide to the Enterprise tries to explain this by stating that some sort of manual adjustment can be made to whatever is in that pedestal. I think it may have been the dilithium crystals, actually. It stretches credibility a bit, but at least it's something. But on the broader point, yeah, even if they hadn't planned in advance for someone to have to go in there, there are twenty guys in radiation suits standing around engineering through the whole film. Scotty was even wearing the radiation gloves that Spock ultimately used. No one even needed time to change clothes. Just put a helmet on and go. Again, the idea that engineering would be wholly unprepared to deal with a catastrophic situation such as that, and that the science officer would need to come down from the bridge to fix it, is also ludicrous.
