Jaws of Hakkon Quest (It remains to be seen)

This happened to me as well.  I didn't want to look at the forums until I went through the content to avoid spoilers.   Now that I finished everything you can do there, I figured I'd peak to see if anyone else ran into that issue so that I can help with the work-around to get the quest back on track that I discovered.

Let me tell you how I got this error and how I fixed it.

How I got it:   I roamed around, explored a lot,  and seemed to have completed things in a different order than Bioware anticipated most gamers to follow.  If you did something similar, this is most likely why it is seemingly bugged.

However there is a way to correct it.

Here's what to do:  Go to the swamp, look for these lantern looking things and you will be able to interact when close.   It says that you can collect the relic --- all of the sudden you should get an update with another objective for that quest.   Once you finish there, it will tell you to head back to the Augur.  Go back there and talk to him, which should complete the quest.  He will ask of you to go check on something that you most likely already did (which I think is what bugs it --- I took Veilfire to their hold and stumbled upon the three items he will then lastly asks you to look at).    Once you are finished talking with him, your quest should end.   The Veilfire will now be active in his house for you to use (previously it was not for me most likely due to the order I did the quest), however there should be no further communication with him other than the typical NPC dialogue even if you go to check them once again and return to him again as he asks... you already heard that dialogue if you viewed them with the Veilfire before obtaining that part of the quest from him.

So yeah, they should make it so that it registers when people do it in their own order, however it seems it was overlooked.  No big deal, that worked for me and it completed the quest.

I'm being a bit vague with the exact items/dialogue in the fix I listed just in case someone reads this and doesn't want spoilers.... but go to the swamp, find a lantern that you can interact with, then follow the directions to complete the quest.