A proper quest log is indeed one of the more puzzling omissions in D4. It just seems so obvious to have such a feature in a game where you can do a multitude of quests, and yet here we are.
Right now your best option is to use an interactive map and track your completed quests there. Most of the sidequests are given by NPCs, so those are easy to check. Yes, you’ll have to revisit a bunch of areas, but at least you can see the where the questgivers are on the map immediately, and mark the quest as completed if there’s nothing there. Keep in mind that a few quests only show up once you’ve completed the campaign, this includes some of the found ones as well.
As for the remaining quests that need to be found in the world, I would suggest that you consult this great thread, as it has helped me finish off the last few ones that I was missing.