Edit: I thought that it was possible to interact with NPCs of other worlds, thus completing other ppl quests. It is not possible.
Edit 2: I looked into it, and it's possible to access quests from other worlds in the Arena's NPCs. Cowbeans changed the quest of the right one to be equal to the main quest (the one of the inventory), before was medals. Deal is that it's not available in worlds of other players (right NPC). The left NPC on the other hand (medals quest) is accessible in other worlds. I didn't complete any task yet so I don't know if it syncs with the one of your main world, who knows.
Other thing I noticed is that completing quests does not take your items, just require that you posses them to complete the task. As far as I remember before it consumed the items. Good change!