I would have rebalanced the dragons, made them smarter (dont fly off when they are close to killing you or an enemy). I would have made them more challenging, the first one killed by the dovahkiin and a larger band. Then revealed to the player that he is dragonborn, and that he gets a big buff vs dragons (double damage or whatever).
Rebalanced the levelling so that you wouldnt go from lvl 1 to 20 in 1 hour by letting an enemy punch away at your armor. Experience works much better than going from 1 to 20 by casting muffle 100 times.... etc. Quest experince would have made the quests much more worthwhile.
Rebalanced the combat, its fun until you are high level when no enemy gives you a challenge at all. I love fighting bandits when im around level 15, by the time i hit 30 everything in the game is a joke.
Added more good quests, and diffrent quest solutions. Would have made it possible to remove quests from the quest log.
Some things at the top of my head.
Oh and Skyrim is still one of the best games ever made.

