I'll try to sum up my current understanding of the bug and my current investigation status in a clear manner.
The bug itself:
Mission tasks register as Sims perform them, but when all mission tasks are complete:
1) The tasks are being checked, but not removed from the Mission (Career) Panel.
2) Mission Complete notification does not appear.
3) The Sim does not get Batuu Credits for the mission.
4) Traveling in Batuu afterwards causes all current Batuu Credits to disappear.
Sims new to Batuu:
Currently known bug triggers:
1) Sim has a Fine Arts degree (any of the 4 variants).
2) Sim has the Business Savvy trait.
I have tested both triggers with my current Sims and with new Sims (with no other skills/traits/completed aspirations inside a new game.
[Cheats were used to both add and remove those triggers (can't remove those with game play, anyway)]
Known trigger not yet reproduced:
1) Ancient Bloodline trait.
I was NOT able to reproduce the bug by adding this trait with cheats to a new Sim. I am currently working on testing this through game play.
@lcomp12was able to clear the bug by removing the Ancient Bloodline trait (with cheats - again, no other way to do this).
Other traits and degrees, as well as skills and completed aspirations that I've tested do NOT seem to affect the bug. While I haven't tested all of them, I have covered most of them. With skills, I have tested all but Medium. [I have not included toddler and child traits, nor did I try to send a teen to Batuu]
Sims returning to Batuu:
Since I only started playing with Batuu last weekend, I have no investigative data on that yet. Also, it is not always clear to me if Simmers report Sims who are returning to Batuu, or are new to Batuu.
Currently Suspected Triggers:
1) Occult Sims
2) Mermaids
3) Magicians
I highly suspect that these triggers are still relevant for returning Sims:
* Fine Arts Degree
* Business Savvy
It is possible that simply returning to Batuu is a trigger, regardless of non-Batuu status, but it's just my suspicion.
This only represents my current understanding of the bug, as far as I could gather from what other Simmers have posted, as well my own experience and testing.
Regardless, as far as I'm concerned, this is all the same bug. It may have multiple triggers, but it ultimately has the same presentation - Batuu Missions not ending when all tasks complete.
I do NOT have the following packs: Dream Decorator, Laundry Day, Paranormal, Kids Room, Toddler, My First Pet, Throwback, Country Kitchen, Courtyard, Bust the Dust.
[Obviously, I cannot attest or test whether or not the bug existed in previous versions, or how Sims who already interacted with Batuu in previous versions are affected]