ArenaNet talk:Guild Wars 2 suggestions/Show completed quests
It is a good idea to see what quests you have finished (completed are those which you still have to take the reward for it), but not for the reason of seeing what you have done.
I suggest that if one character has finished a quest but now he is helping other players finish that quest too, he will be able to select it from the "finished quests log" and be able to see the "quest markers" again so he will not be forced to remember the course of it. There will be no experiience points or awards for him after finishing it except that obtained from killing monsters on the way.
I believe this way, players can go "farming" with a reason: -folowing the quest again and not just farming random arias -doing each quest again in Hard Mode after unlocking this mode