There is no way to retroactively find out which quest you haven't done.
Not until Blizzard adds UI interface functions to access the quest database.
E.g. QuestHaveDone("quest name").
The best advice I can give you - start in the starting areas and work your way outward. If you run into places where you've done quests, move on to another area. If you need help figuring out what quests you can or can not due. questkeep.com and thottbot.com can help with that.