I saw that old quests were reappearing in journal and was very excited. The Cuba Teleportation quest vanished out of my journal some time back when I was only halfway through.
So I logged back in, the quest was still at where I'd been when it vanished. I finished killing the remaining gators (the flytraps I'd previously completed, but that part was not showing in the journal
https://prntscr.com/fdhutm ) and visited Tia Dalma and redeemed the quest. Got the "good job" message and received 525 notoriety points. There was still a green circle around Tia so I foolishly clicked it again. And got the TP quest all over again. Did not have TP ability for Cuba. So I had to start the quest over again.
Then I leveled up my doll during the 2nd attempt and all side quests (including the Cuba TP, erroneous Doll quest and Rudyard's Teeth) disappeared from my journal. Relogged, got all of the quests back in journal, but as if I'd never made progress...had to go back and receive the quest from Tia Dalma and start over again. Finally managed to complete the quest and get Cuba TP. Got the 525 rep again, so there's a potential exploit. You could keep completing that quest (as long as you don't level a weapon in the process, thereby stopping your quest progress), turning it in and turning right around and accepting again, getting 525 rep for each completion.
Still have the doll quest, even though my doll is at level 10 and the Cuba TP return to Tia message is still in journal. No biggie.
Went and got the Rudyard's Teeth quest from Jack. Kill 25 Duelists. Was approximately 1/2 way through when I leveled my cutlass and the kills stopped counting. Checked and sure enough...all side quests had vanished from journal.
Re-logged and they were all back, and all at 0% progress. "Visit Jack Sparrow to receive Rudyard's Teeth quest".
During all of this there were random crashes, and having to relog multiple times because I was having to sail to Cuba and porting under the island. In the process I switched servers several times, but had the same results on all servers when it came to leveling a weapon during quest causing all side quests to vanish.
Never lost the BP quest, and that progress remains at correct completion amount.
*Edited to add that completing Rudyard's Teeth quest does not reward the 100 rep and reverts to a new quest status once you're done with it. Now Doll, Cuba TP and Teeth quests are all still in journal as new quests.
tl;dr - leveling a weapon during Cuba TP or Rudyard's teeth quests will wipe all quests (other than BP quest) from journal. Cuba TP quest can be completed multiple times, receiving 525 rep for each completion.