Star Trek (film)/Wall Banger

The Star Trek movie that rebooted the franchise had some problems:
 * Kirk's promotion at the end of the film. While the Status Quo Is God (and it was completely expected that Kirk would become Captain), it's still a bit ridiculous that a man in his late 20's can be promoted to Captain of the Federation flagship.
 * The plan to destroy a supernova with a black hole. Supernovae create black holes in the first place. And if the supernova manages to destroy a planet in another star system then for this plan to work the event horizon of the black hole would have to be several light years in radius.
 * Also, how did Spock run out of time? Even if the supernova's shock wave were traveling at the speed of light, the Romulans would have seen it coming years earlier and been able to predict almost precisely when it would hit. Why didn't they evacuate at least?
 * Your average Federation captain know the "frequencies" to avoid Earth's defenses. That kind of makes sense, giving a ship's captain the ability to not get shot up by your own defense network. However, these same Federation captains, in no less than two separate instances, have flown over to a hostile enemy ship to "negotiate" with the attackers. Captains, with critical information that would allow an attacker to bypass Earth's defenses, going alone, to a superior enemy's ship after being attacked by them. The Narada ends up getting through Earth's perimeter defenses completely unmolested later in the film.
 * Easily explained by Nero's Complete Monster tendencies. He would quickly and remorselessly destroy several Starfleet ships if he didn't get what he wanted. If the captains didn't go over there, it's possible that he would have blown up the ship, then found another one, rinse and repeat. He definitely doesn't have any qualms with blowing up a planet, and it's doubtful an interplanetary vessel (such as the Kelvin or the Enterprise) would receive as much consideration.
 * Why did Nero need Earth's defense frequencies anyhow? The Narada had just managed to destroy a flotilla of top-line Federation capital ships with no perceivable damage at all. The only reason is that he's either running out of missiles (it is a mining ship after all, and probably doesn't have all that much military hardware), or doesn't want to risk getting rammed again.
 * "Get him off this ship". Ignoring the fact that Federation starships have always had something called a brig, specifically for the purposes of holding prisoners and insubordinate crewman (ideally so they can be court marshalled later) jettisoning Kirk to this ice planet (which as Mr. Plinket points out, does not exist in Star Trek) would have been a death sentence, effectively making the new version of the Spock character we're made to sympathize with, a murderer. Not one character in the film calls him on this.
 * To be fair, Spock puts Kirk within walking distance of a Star Fleet base, and provides him with survival equipment. And McCoy does call him out.