#1 Random Encounters
Morrowind had a lot of quest hooks roaming the wilderness, but they were something to find once, not recurring. In Oblivion you could fast travel everywhere guilt-free because there were absolutely no worthwhile diversions between you and your destination. In FO3 however, there was always some unexpected bit of story or emergent gameplay lurking around the next corner. I hope that in future TES games there will be a deep enough supply of random encounters that I can never confidently say "I have experienced everything interesting in town/region X".

#2 Quests without invitations
In a lot of places in Morrowind and Oblivion, you'll find something cool, with an NPC idling next to it, but you don't get any dialog topic to talk about the cool thing unless you happen to already be on the quest to find the Cool Thing ™. In FO3, if you stumble across something interesting, you can get involved right on the spot. To be fair, this is mainly because of the general lack of factions or multi-step quests in FO3, which is not something that should carry forward into the Elder Scrolls. I hope that in future TES games, if you stumble across a quest objective you will be able to perform the quest on the spot even if its normally in the middle of a 15 quest series, or if that's not possible, at least get a dialog topic so you can find out where to start the chain.

#3 Dialogue trees, not topic lists
Bethesda games have been using a potpourri of dialogue models, where sometimes you are picking from a library of words to ask about, and other times there is a scripted set of actual dialogue trees as seen in classic BioWare RPGs. The proportion has been shifting towards trees over the course of several titles, and hopefully it will settle 100% into that style for the Elder Scrolls. Whatever you do, please do not go the route of having presumably illiterate players pick "moods" rather than actual dialogue lines, as BioWare and Obsidian have been experimenting with.

#4 Humans that look human
Between Oblivion and FO3, someone figured out how to use Facegen. Make sure you don't backslide.

#5 NPCs with lots of personality or none
People with names either have a quest or something unique and entertaining to say. People generically named "settler" are there to make the place look more lived-in. Use this delineation in the Elder Scrolls as well to separate notable NPCs from those that are just there to chat about mudcrabs. Don't skimp on the number of named characters and associated content, though.

#6 Make big cities big
If there's a city of millions in the lore setting, it should either not appear in the game, or take up a quarter of the play area as with DC. Don't mismatch the notional size of a city with its in-game implementation as badly as happened with the Imperial City.

TES should retain what it has always retained from the linear Fallout 3, absolutely nothing.

I'd rather not see perks.

Locomotive animation was mentioned earlier. I don't think it was included in Fallout, but a big yes to that.