It seems some of these have already been mentioned but thought I'd share them as well so that Bethesda hopefully sees that these are legitimate issues.

I have encountered two 'broken' quests so far that have been mentioned several times namely 'Repairing the White Phial' and 'Pantea's Flute'.
In both cases I obtained the items needed to turn in for these quests prior to actually receiving the quest itself and cannot turn them in.
The menu seems to recognize them as quest items so I cannot do away with them (eat, store, drop, etc.) but quest log does not recognize them.

In the case of 'Repairing the White Phial' the quest did not work even when I didn't have a briar heart. I went to the Forsworn camp to retrieve it but a briar heart did not appear as one of the items to be looted from the enemy corpse even though the quest arrow was clearly marked on it. I came across a briar heart later on and was still not able to turn it in.

I would also like to note that I had actually killed these Forsworn enemies before during the 'Legend of Red Eagle' quest. On the same corpse that was supposed to tender the briar heart for the White Phial quest I picked up another 'Red Eagle's Fury' sword. Since I had already done that quest I wanted to toss it but I couldn't because it was still being recognized as a quest item even though I had already completed it.

I have also had to keep in my inventory some of the dungeon key dragon claws (ebony dragon claw, corral dragon claw, ruby dragon claw, etc) even though it would seem I am through with them. I was able to store the sapphire claw in particular but none of the other ones I have collected.

Thanks for reading, hopefully there will be a fix soon as I hate having excess inventory and quest logs but nonetheless thanks Bethesda for a fantastic game.