First and foremost is creating a completely seamless world. What do I mean by this? I mean eliminating the need for loading screens (except of course for fast-travel). When you enter a house, you don't click the door and get magically transported inside, the door actually opens and you walk through. When you go into a mine or a cave, there isn't some artificial obstruction that keeps you from seeing what's down there, you just enter. In Oblivion and Morrowind it always felt strange that somebody had managed to build doors over every naturally occurring cave in the land. This also means you could potentially look through windows in houses and see what people were up to. This would also mark a return to open cities from Morrowind.
What would be the downside? Most likely the game would require a quad-core processor or better for PC and the initial loading time would be much larger. However, I would be more than willing to wait 1-2 minutes for the game to load if it means I don't get my immersion broken every time I enter or exit somewhere. This also means a much more robust and complex 'cell' system that allows for location-based streaming, instead of load areas.
Secondly I would like to see a more interactive combat style much like that of Dark Messiah. This would also include dual-wielding one-handed weapons and mounted combat. This requires a much more fluid and procedural animation system, similar to what Force Unleashed used.
I would also like to see a small amount of destructibility which allows for property damage. If you throw a fireball in a tavern and it hits a chair the chair should either burst apart or catch fire. Either way, you owe the barman a new chair and until you pay, that chair is gone. So the Barman would come at you and demand money to replace the chair and whatever else might have been broken in the process. This would of course only be possible with destructibility.
Lastly, the engine NEEDS to allow for far greater combat AI to be active at once. The 'great battles' in Oblivion were a joke with only up to 15 or so AI in combat mode and the rest standing around, waiting their turn. The engine needs to make sure that large-scale battles (50+) are possible.
What would you like to see improved or added from an engine perspective?