As Uzar9 said, storyline missions you can tell as the icon for them will show if you have done them or not (sword/spear through the icon). Side-quest's unfortunately have no way to tell if you've done them or not, apart from the ! being above the quest giver or not.
I'd recommended opening up either the official or unofficial wiki, going through the quest list's - this way you can quickly find which npc gives a quest, go to that npc and see if a quest is offered - if no quest, you likely have done the quest already.
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