You can say many things about Star Wars the Old Republic, but one thing I really liked in that game was how the entire party was included in the quest dialogues. It made it much less about spam-clicking quest markers - and much more about actually listening and caring about what was going on, at least in the class questlines.
Also, I tend to care about quests a lot more if there's a voiced NPC delivering it - and especially if there's some kind of cutscene involved. Think Secret World here.
What I'm suggesting is that Blizzard goes through all the "vital" quests for the various zones - add a small cutscene, and include a little dialogue or two where party members can comment or respond.
They could do all kinds of other things, including reputation effects based on what you say during these cutscenes - but that's not really the important part of it.
I just think it would make the leveling experience a lot more immersive - and it would be a chance to retune some of the more lore-breaking and silly quests - and turn them into something new for the audience.
Anyway, I think it would be a great way to redo the content and it would be perfect for an expansion.