1. Combat. Boring as hell in Skyrim.
Magic needs to scale damage with levels.
Ranged... IDK. I haven't played enough ranged to know if its decent or not.
Melee needs to have more to it that press button to kill thing. Have enemies block more and better, and have a reasonably significant knockback for hitting someone who's blocking - enough for them to get a quick attack in them get back to blocking. Of course, then the block-breaking heavy attack would become the norm, so more mobility would also be good - allowing you and enemies to quickly dodge powerful attacks.
2. NPCs.
They need to react more to you. If I've killed Alduin, that guy at the companions is going to know me. Same goes for all NPCs. There also need to be some bigger battles going on. There is no Civil war in Skyrim. There are a couple of guys sitting on their thrones telling the Dovahkiin to kill the other one. I want to be wondering the wilderness and coming across a battle between Stormcloaks and Imperials, or going to a fortress and finding out one side is attacking each other. Main towns can wait for Dovahkiin, but small forts and wilderness battles should happen, making the political climate in Skyrim a little more dynamic.
3. AI. Technically this could go under NPCs, but it requires a larger section IMO.
Companions need to be smarter. For one they need to know how to path around traps, rather than walking into the same one 50 times in a row. That's just getting rediculous. Beyond that it would be nice if they levelled up too in stats, but not necessary.
Dragons... Are stupid. They are pathetically easy to kill, and if they're not its not because their smart, but because they are at that point a damage sponge. A dragon should be intelligent, and not land in the middle of a swarm of guards, bears, mammoths, giants, Dovahkiin - ect. It should spend most of its time out of reach attacking you. Flying in the sky and doing fire breathing runs. Picking up smaller creatures and throwing them away. Of course, this makes it hard for melee to take them on at all - hence why you need to outsmart them, or even the field. Near every dragon encounter, have a dense forest or something of some kind - a rock overhang, a cave - anything - that the dragon is unable to just fly over and breathe fire at you from. It needs to land to attack you, and thus a melee or stealth character is now able to engage it.
And of course normal unit AI would have to be updated for the new combat system.
4. Stats. I like stats. They are a quantifiable measure of different aspects of your character. I don't think "Health" "Stamina" and "Magic" are all that you need. Strength, Agility, Dexterity, Fortitude, Intelligence and Wisdom are some things I'd like to see. Of course, this can lead to forcing players to build character in a certain way to have a chance at winning the game, so I say for lower difficulties have an abundance of skill points on level up, allowing a player to really make their character whoever they want them to be and still be able to push through the game just fine. Higher difficulties reward less points for levelling up, forcing players to become more and more specialised each difficulty level to remain effective. What I'd have them do;
Strength: Increases damage with swords and bows, increases amount of damage blocked with block.
Agility: Increases running speed and dodging speed [Or whatever manouvrability is used to allow you to evade heavy attacks easier], decreases Stamina cost for running, jumping, dodging and other movement related acts.
Dexterity: Increases the rate at which you can attack and decreases Stamina cost for all combat related acts.
Fortitude: Reduces knockback from heavy blows and from attacking someone using block, increases maximum Stamina and Health.
Intelligence: Increases damage of spells, and Magic Regeneration rate.
Wisdom: Increases damage blocked with defensive spells and increases maximum magic.
5. Interface. Needs an overhaul.
Easier to set hotkey buttons, more informative pages, better layouts and names/labels/sorting of items - ect. Basically, what was done in one of those mods I remember having before I uninstalled Skyrim. At its release state, its utter crap IMO.
6. Polish. IMO, Skyrim lacks it.
Bug fixes ahoy! I've been locked out of too many quests and abilities to become a Thane now thanks to bugs. No doubt they've had some of them fixed, but there were way too many.
Also, not sure whether its a bug or not, but for me horse salesmen never got another horse in. Lose 5 horses in Skyrim and you'd never be able to get another one for the rest of eternity unless you stole it from some soldiers, at which point it'd just screw off after you jumped off it.
Some nicer shaders could also be good. More of a minor thing now that the textures have been officially updated, but they game could - and with mods does - look a LOT nicer.
Those are probably the main things I'd change, though not the only.