I really liked the film and most of my tweaks would be little fanwanky scifi and military nerd things, but why not:
1) A line of dialogue that suggests the Narada was being repaired and refit in those long 25 years (since people seem so obsessed with this mystery.)
2) after their confrontation, Spock first orders Kirk to be thrown in the brig. When McCoy informs him that the brig was destroyed in the attack, Spock says "Very well" and the next shot is of the escape pod being launched. (My reasoning - marooning seemed a little daft as a first resort, even for young angry Spock.)
3) the planet Kirk lands on is announced to be T'Kuht, sister world of Vulcan. (Just as fanwanky as Delta Vega, plus it actually makes some modicum of sense!)
4) Spock recalls how the Hoban star threatened Romulus (not the whole galaxy). While he was on the way with his ship, the Romulan military attempted its own solution - which resulted in the warp-speed shockwave we see in the film. (it would be foolish to include the technobabble in dialogue, but I would have used the VFX for subspace weapons, thereby ensuring some ubergeek could earn cred by comparing screenshots to INS.)
5) Others already suggested something along these lines, but I'd do it like this; when Kirk offers Nero rescue, the Narada reaches out with those big metal tentacles and tries to pull the ship in with it. (Come on, wouldn't it be nice if those things actually did something? Plus the visual is nice.)
6) I really would have preferred Kirk to be first officer under Pike, but I do sympathize with the studio's desire to make him captain. A little fig leaf would have been nice, though - perhaps the Starfleet brass do it on Spock Prime's specific recommendation. "Alright, we did what you wanted. Now, tell us about this V'ger thing..."