I was able to successfully complete every quest in Ghrahtwood, granted this was a few days ago. This may or may not help you, but usually relogging once or twice fixes the quests -- by relogging you'll usually end up in a different instance. You mentioned playing since Beta so you probably already knew/tried that, but just in case...
Heart of the matter still bugged the quests are atrocious considering eso is attempting to coax newbies into memo so frustrating coz I just love spending 45 mins of my time doing quest twice to find out no bug fix 1 week after first reported
I completed all the quests there (other than Goldfolly, where I never found the quest starter). However, it took multiple relogs to fix phasing issues on most.
Snit AD Sorc Ratbag AD Warden Tank Goblins AD Stamblade
Heart of the Matter still has an issue (no soul essence to absorb).. I have re-logged multiple times. I am going to try dropping it and re-taking it but it was such a long line I hope I don't have to start COMPLETELY over.. -_-
Assassination/ Dual Wield Specced Stamina-based Nightblade, because I like Hardmode apparently Twitter | Raptr | Twitch.TV
Greenwoods does not really improve, many of the quests are bugged. I could not even abandoned one to start over, I put a bug in, and when I logged back in the Quest was reset and i was able to finish it fine. I think one of the big mistakes was not having an open beta that allowed players to go further into the game. This game launch reminds me of EQ in a lot of ways, which in my opinion is a step backwards in some cases. This game is plagued by what I think is caused by a publisher who wants to get a product out the door and figures x bugs per line of code is acceptable.
With today's MMO market a loss to another game even a small loss can amount to millions.
I did Grathwood a week ago, three quests with problems,
first was stopping an ceremony in the staring city in southwest, logoff and login solved it.
one where you had to fight a ghost outside on an Ayleid ruin west of capital, and it did not spawn, return later and it worked.
Second was a Argonian village in the south who was bugged until patched.
Had 4 broken quests in Adudin who took multiple tried to work.
ESO has an engine problem if too many people tries to do a quest at once.
To an large degree this can be patched but don't show up until pressure is to large.