Discounting silly technical things like graphics or AI (which of course are going to be enhanced for Skyrim), I don't want:
Swing-and-miss gameplay: I'd rather skills be handled like how Alpha Protocol does it. You can hit, and do basic damage, with most any weapon, but, for example, you won't be able to line up a headshot from a room away using a pistol if your skill is too low, you'll just do the basic hit. Or in terms more relevant to the Elder Scrolls franchise, you would be able to hit and do minimal damage with any sword you find, but improving your long blade skill, for example, you'll do more damage, unlock new techniques (power attacks, be able to differentiate between slash/chop/stab attacks, duel-wield, etc.), and generally be more effective.
Generic dialogue: Sorry about this one, mates, but I never thought the dialogue in Morrowind felt at all natural. To go up to a Dunmer and have him say "Speak quickly, outlander, or go away" and then open up the text window and see "Certainly, I have a moment. What's on your mind?" or other pleasantries felt really awkward. And it was even worse, having every noble, slave, commoner, shopkeeper, and thief reciting the exact same encyclopedia entry on Balmora, the Dunmer, or one of the three "little secrets" that the game was kind enough to provide, and then trying to find a specific topic in that mass of random junk was a nightmare as well. I'd rather the games err on the side of having too little to say than too much, because when it comes down to it, how often do you give lectures to random strangers on topics as varied as your home city, your family, or your profession?
Creatures: I love Morrowind with all my heart, but it's its own game, and Skyrim is it's own game. They're two totally different provinces, and I don't want to see the developers trying to shoehorn anything in that doesn't make sense in a misguided attempt to please the fans. That means no snow guars, no glacier racers, and no giant bugs.
EDIT: Yes, and Levitation as well. It always felt like a cheat to me, like I had just opened up the console and typed "tcl"