Revealing mistake: When Kirk and Kruge are fighting, a piece of the cliff breaks away and wiggles down the side of the cliff rather than falling like a rock. (01:22:55)
Captain Spock: My father says that you have been my friend. You came back for me.
Kirk: You would have done the same for me.
Captain Spock: Why would you do this?
Kirk: Because the needs of the one... Outweigh the needs of the many.
Captain Spock: [begins to remember] I have been and ever shall be your friend.
Kirk: Yes. Yes, Spock.
Captain Spock: The ship... Out of danger?
Kirk: You saved the ship. You saved us all. Don't you remember?
Captain Spock: Jim... Your name is Jim.
Kirk: Yes.
Trivia: At the beginning of the movie Kirk rescues McCoy from a jail of some sort. Before leaving Kirk asks McCoy how many fingers he's holding up and does the Vulcan hand thing. However, Shatner had severe difficulties putting his fingers into place, they just wouldn't hold into position. So the crew wound up wrapping fishing line around Shatner's fingers, he would put them into position out of the camera and the shot quickly jumped while his fingers where still in place. If you look closely you see the line around his fingers. (Note that this problem occurred several times during Star Trek, actually, Nimoy and Leonard seem to be the only people doing this without a problem.)
Chosen answer: Kruge only had the proposal video that talked about what Genesis was. He didn't have any actual data on how Genesis works or how it could be created. Having footage of a nuclear blast doesn't give you knowledge about how to build a nuclear device.