I've just seen the film for the third time. All of my friends know me as the big Star Trek fan, so I've been getting invited to this one a lot... The film really stands up to repeated viewings, but that didn't deter me from trying to find multiple plot holes and ways the film could have improved.
I'll point out a few, and also muse on some things discussed in this massive thread:
1) What really sticks out to me on this viewing is Scotty's line. "One day! I've been off this ship one day!"
Did we really need to have the need to have the whole adventure take place in a 24 hour span? This makes the voyage to Qo'nos implausible, which of course it is, and diminishes sense of vastness of outer space. But it also is a missed opportunity.
There's a scene that just before Spock confronts Carol Marcus about her identity that shows the Enterprise at warp which could have made it an indeterminable amount of time. It would have been an ideal moment for a Captain's log. Something to the effect of : "We are enroute to Kronos and will reach Klingon space by tomorrow. The crew is preparing for the mission with focus and professionalism... " etc. It could have provided a nice act break and the scene with Spock and Marcus could have followed seamlessly.
Scotty's line could have been changed to "One week, one week I've been off this ship!"
It also would have provided Scotty with more time to learn the Vengeance's systems and allow him to sabatoge it to the degree that he did more plausibly. I don't think it would have detracted anything from the plot, but would have closed some plot holes nicely.
2) Carol Marcus did not say "Transwarp"... she said "My father has been developing advanced warp technologies." Just to clear that up if it hasn't been done already. Seriously though, as others have pointed out. If they had stayed at Warp .000000001 second longer they would have overshot Earth by millions of miles. LOL. I really don't have any explanation for that. Why not just have them arrive at Earth, and have the Vengeance attack them as they attempt to hail Starfleet?
3) If the Vengeance could beam Carol Marcus off the Enterprise when it had its shields up, why did Khan need to argue with Spock over the torpedoes? How did the Vengeance beam Marcus off the Enterprise with its shields up anyway?
4) I thought Uhura's confrontation with the Klingons was brilliant--up to the point where the officer grabbed her neck and pulled the knife. Her appeal to their honor REALLY made me appreciate her as a character and the writers understanding of Klingons. Then they made the Klingon guy a typical brute. The scene could have been even more effective if he did clutch her neck and say, "We'll find this human you are looking for and teach him the price of violating our territory, just as we will teach you." and then have Khan go apes--t on them. At least that way, it could have seemed as if Uhura MIGHT have been able to talk her way out of it, rather than her plan falling apart only to be saved by the sheer luck of Khan's interference.
5) How does 1 photon torpedo Destroy General Chang's BoP in ST6, but 72 photon torpedoes blowing up INSIDE the Vengeance only "disable its weapons systems"? That thing should have blown to Kingdom Come. I don't really know an elegant way to have fixed this in the script so that the Vengeance could still be piloted to collision course with the surface... Maybe Bones was only able to arm 3-4 of the Warheads in time? Even so, an ordinance explosion of that magnitude within the hull still takes most ships down.
6) I feel like one line added to the scene with Bones discovering the Tribble was alive could have fixed a loose end. I discussed Khan's blood with a friend and we both wondered why they couldn't have used the blood of one of the 72 other superhumans they had on board? We both agreed that perhaps the blood of those still cryogenically frozen wasn't viable to use in a serum and would take too long to thaw out. An additional line from Bones to that effect would have been helpful.
7) The scene where the matter-anti-matter injectors are misaligned and Scotty forbids Kirk that they can't open the compartment or they'll both be killed before they make the climb... for some reason, in this latest viewing reminded me of "Thine Own Self" where Riker tells Troi, "My first duty is to the ship..." I wondered why Scotty didn't attempt to enter the core in an effort to save the Enterprise from certain destruction... and why Kirk didn't order him to...
Now to me, Kirk's heroism in that scene(the beauty of the set, the raw physicality of it, his fear in the face of certain death, which he FINALLY felt) was the best moment of the film, and one of the best moments in Star Trek. Still, I wonder if I would have liked it better if Scotty had said "I have to make the climb." and Kirk says his line and knocks him out.
I enjoyed the movie immensely, and these plot holes are more little annoyances than major problems in the plot. I still feel like Marcus's corruption and outright disregard for his own people was the biggest issue with the story.