As you guys probably figured out by now, these 2 weekly quests, that require you to farm 1500 honor in an Epic or Random Battleground, are bugged.
How are they bugged you ask?
They are bugged ONLY if you already have 15000/15000 (capped) honor. If you have capped honor, the quest will not progress and will sit on 0/1500 regardless of how many battlegrounds you do. This means that you literally have to spend at least 1500 honor to free up your cap before completing the quest to circumvent the bug.
So right now, if you want to do this quest but already have capped 15000/15000 honor on your character, make sure to spend some honor on a vendor before queueing up.
Note that this quest bug does not happen for the weekly Arena quests. Even if you are honor capped, the weekly arena quests continue to give progress to your quest for each game you played.
Please fix this bug, as it leads to people wasting their time into being forced to leave a battleground to spend honor. Many people don’t even know the fix and just assume the quest is bugged by default or simply don’t understand why they can’t get progress on the quest.