Minor visual bug here. But if you have a New quest, the “New” will stay on the screen even if you open an item window as shown below, see next to the ring on the left. Can be fixed by closing the quests list, then opening it up. The New is still there, on the quest list, but doesn’t stay on top.
EDIT: Just in case this is related a specific quest. It was Amoury Aid, Find the Armoury.