Alchemy: Liked the feel of potions in The Witcher (much longer durations, but had a "toxicity" concept that prevented you from using too many at once). The oils there were much more useful than poisons in Oblivion, and bombs would be a nice addition. The requirement for potent Bases and numerous reagents for powerful potions would be another useful balancing tool. However, it didn't have the flexibility of creating your own potions, which would have to be addressed. Liked the Research concept from BS2, and think something similar (involving combining ingredients rather than damaging enemies) would be great for Alchemy.
Quests: Daggerfall's random quest system would be nice; not for important quests, but more as a way to earn money and skill through your guild without aimlessly wandering around. That is, as way to be a full time Fighter, Thief, Assassin, Gladiator, etc. Hunting bounties, guarding caravans, assassinations, gladiatorial fights, chariot races, courier deliveries, targeted burglaries, all fairly straightforward repeatable quests. Mages aren't well represented, but research could be sort of a freeform quest system for them, if ingredients tended to be found in specific remote locations. Also, mages could have "country doctor" style quests for alchemists and restoration specialists. I suppose enchanters could also have "quests" that require them to create specific enchanted items for NPCs (that would typically be useless to PCs -- an Enchanted Broom of Sweeping sort of scenario).
Alchemy: I hated the silence and paralyzation, which duration was always too short. When i'm at skill level 100, i want to be able to have someone paralyzed for 60 seconds so i can take out a group of spellcasters or marauders with my low-health stealthy thief. More potent potions at higher levels would be nice. (Side-note: bombs involving alchemy would lead to gunpowder eventually.)
Quests: Big hooray if they would re-introduce that. I always felt looting bodies as very necessary to gain gold in OB, with the carrying capacity being rather low it would take lots of time to buy a house. There are mods like wonderdog's purse of wonder to 'increase' it, but a regular job to make money is more satisfying. And also, mages guild quests involved getting "mummy wrappings" (And of you went to defeat a lot of undead.) It also involved casting a spell on someone who couldn't sleep or to deliver some research from one place to the other while being chased by necromancers. (I've just played a lot of MG quests in DF)
And to add a theft from other games: "The bag of holding" with limited capacity and explosion effect if another bag of holding is put into it (from various games i can not remember the names of).