In World of Warcraft: Mists of Pandaria, Blizzard have discontinued the model of using faction tabards to level reputation levels for each faction, and instead removed some of the daily quest restrictions.
I have also noticed that killing trash enemies in dungeon instances no longer gives a steady stream of reputation throughout the instance, but that there have been some larger chunks of reputation added during the course of each instance (unsure what causes this, but suspect it to be bosses).
With this in mind, what is the fastest way to level faction reputations? Is it just a case of grinding daily quests or is there a new replacement mechanic for tabards?