I see there is a check box by the quests as listed in the Journal... only have one right now, so having it "selected" or not seems to do nothing... logically, it SHOULD mean it is displayed in the UI, while unchecked it doesn't.

But I AM curious what is meant by "You can mark them in the log to prioritize and kick out finished ones that you no longer need to show up." I surmise if you "kick" a completed one out, you lose the fact it is completed, and thus lose any rewards from it.