#1 - April 22, 2016, 1:31 p.m.
Earliest examples were Captain Volo'Ren and the Cage of Infernals event with the Infernal Lord in Azsuna, those got fixed as far as I know. But it seems to be a general bug that needs fixing and is present on more than half of those quests, especially those with blue background on their icon.
It was even the case for the Soultakers-World Boss Quest. I simply completed it by dying and leeching after tabbing while a full raid of people did not get credit for the quest and did not know exactly why.
Latest encounters of this bug for me included WANTED: Glimar Ironfist and Wanted: Hannval the Butcher (although I knew that the later was bugged because it has been active before, but why not try?).
If you look through the World Quest- and Bug Report Forums, you will find many topics for "WANTED:" quests and other similar quests.
Please revise those quests and fix this bug, as it will simply lead to more and more players intentionally dying while other players finish the mob the more known it gets.
PS: Hannval in particular also seems to be very picky where one is allowed to stand to have the World Quest for him active.