This thread is full of awesomeness.
My 2 cents (crazy stuff):
Warfront: A special open world zone, maybe somewhere around Ala Mhigo, where large scale battles between players and Garleans would occur on a regular basis. Or even, the same idea applied to Ala Mhigo itself making it a contested area.
Winning the battle would free the city until the next attack (kind of like besieged).
Airship battles: Eorzean airships assaulted by Garleans airships. When the Garlean airship is taken down it crashes on the ground and players can enter the wreckage to kill crew survivors and get some Garlean loot / technology. This could even go as far as be part of a large scale quest to study / acquire Garlean technology.
Enemy territory: Zones in Garlemald (Expansion?) where players would have to assault camps and then defend them from retaliations to get benefits from them (aeterythe, supplies, guildleves...). One step further, assault Garlean cities directly. Garleans would roam the zones to kill players (like behests where players are the mobs

)
Invasion from below (raid): A huge, huge underground dungeon containing some kind of portal that would pour in monsters. Players would have to enter the dungeon, kill the monsters and seal the portal in a limited time, or else they would invade the nearby open world areas.
Traps & secret doors: Place all kind of traps and secret doors in dungeons where it makes sense for them to be and make abilities available to thief-like classes to disarm / discover them. They would be dynamic and their location would change everytime. Secret doors could open special, dynamic, instanced dungeon parts.