Oh, I have plenty of ideas of how to improve it. I appreciate yours!
Pondering this, in addition to leaving out Chekov until the sequel and including the ladies, I would probably have:
- Used a 'subspace shockwave' instead of a supernova (which can only travel at the speed of light). Sloppy use of real physics offended the 8 year old I went to see it with.
- Featured Number One transferring to command one of the other ships, giving Lt Spock the chance to become first officer.
- Not made Nero's ship ludicrously invincible but use gravitational waves to damage the fleet and a cloaking device to escape. TWok was way more interesting with more evenly matched opponents.
- Added a line of dialogue, probably from T'pau, about a plan to help the survivors before Enterprise abandons Vulcan.
- Had Nero destroy the local subspace network so Spock's plan was to get within range of a relay to contact someone who can contact the fleet rather than flying all the way there at low warp.
- Had demure Rand be the one to catch Kirk off guard and take him down on the bridge instead of Cupcake as an homage to her mistreatment in Enemy Within.
- Had Spock beaming Kirk to the brig on Delta Vega accompanied by Yeoman Rand as security escort. Spock Prime onsite assisting Scotty to develop a transporter capable of getting past gravitational distortion and a method of penetrating Romulan cloaks. Spock shows Scotty how to do transwarp beaming (much shorter range) but Kirk and Rand have to brave snow monsters to modify the emitters.
- Had Enterprise bait a trap in the solar system to penetrate the cloak, and a security team plus Kirk and Spock to beam on board. No snogging on duty during a crisis, just a bit of suggestive finger rubbing.
- Avoided summary execution of Nero. He tries to torpedo Kirk and gravity pulls them back to destroy his own ship. Symbolism.
- Not had them jetison the warp core, the ship would just be re-caught in the gravity well seconds later due to drastically reduced power output. Full power should be used to create a slingshot.
What the Kelvin movies did well was maintain an exciting pace with some ongoing themes and character development. I think new TOS would struggle to stay relevant without ongoing plot elements. Self-contained episodic TV doesn't work as well these days although CSI fans may disagree.