Escape from Reaper's Eye:

Call to Arms
If you ask the Seekers to wait after killing the Shriekers, they will get bored very quickly and run off to take the ship without progressing the quest in your journal. "We left Reaper's Eye without the help of the Seekers."


The Arena of Fort Joy
Arena quests are left open for PVP reasons (those are the companions you can fight, for anyone wondering why it won't work with normal NPC companions). The game will still acknowledge you as the champion post Fort Joy; your main character will have a tag added [Champion of Fort Joy]. "We have ventured onwards[sic], without fully exploring the fighting arena of Fort Joy."


The Burning Pigs
If the Seekers have moved to the Abandoned Camp before you bless the burning pigs, they will never show up at the sanctuary and you can't progress this quest. As far as I know, but I may have missed something. I looked far and wide to find where they ran off, and I was unable to find them after this sequence of events: (1) blessing the first burning pig to extinguish it, (2) killing Scapor who showed up at this point, and (3) blessing the remaining pigs I could find to extinguish them all; they all run off right after they are blessed before I can talk to any of them. There is intended to be dialog for you to send them to the sanctuary, and then they will ask you to do another task for them. Another factor may be that I caused a lot of explosions earlier that made them lose reputation with me; maybe I was too hated without realizing it, so they didn't want to ask me for more help. "We left Reaper's Eye without helping the pigs."


The Imprisoned Elf
If (1) you are the Red Prince, and (2) you told Stingtail (the real thief) to use the drudanae (from the stolen oranges), then (3) you kill Griff to free the elf, this quest will never acknowledge Amyro being freed. Issues here might also have something to do with allowing Sebille to murder Stingtail. "We have escaped Fort Joy and abandoned Amyro to his fate."


The Purged Dragon
Slane will come to help you in the battle with Alexandar; if you have already beat Alexandar before freeing Slane. "We have left Fort Joy behind us, and Slane as well. He'll have to save himself."


Withermoore's Soul Jar
The freed Withermoore will show up to help you in Braccus Rex's vault if you have already solved it. "We have left Reaper's Eye behind, without helping Lord Withermoore."


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Finding Emmie
If you have pet pal, and talk your way out of fighting the dogs, then this quest remains open. The only way I know to complete this quest, is to kill Emmie; I could not find a way to make her come with me back to Buddy.


Every Mother's Nightmare
Issue: If you speak to Jeth first, speaking to Fara after does not provide any way to resolve this quest.
Solution: Speak to Fara with another party member. Also, if you asked to see the doll, you can later sell it back to Fara if you feel bad leaving with it (for a modest fee, or offer it for nothing in return if you are a bleeding heart); I couldn't find any way to use it to talk to the ghost of her daughter or anything (and for some reason it was flagged as stolen).


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A Rare Prey and The Tribe of Saheila are ongoing, so they intentionally do not close.

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My Story So Far: The Covenant and The Magisters are ongoing quests.