Imagine a place like the argent tournament where players come to compete and prove their skills. You can select different challenges (tank, dps, or healing) and then you have to prove your ability in combat. You're placed in a phased arena with NPC teammates and you have to win against the other team. PVE style combat, not pvp. If you select the tank challenge then you have to aquire the aggro of the enemies, hold aggro while your team dps's and survive the encounter. The dps challenge would simply require you to do enough dps to take the other team down before yours goes down with some mobs becoming immune to force you to switch targets. And there would of course be fire you have to move out of. The healer challenge would consist of you keeping the NPC tank and dps alive.
Completing the quest would award you with the "Beginner tank/healer/dps of Northrend" achievement and lead to a second quest where you have to do pretty much the same thing but its harder. There could be multiple levels of quests resulting in achievements such as "Grand Master tank of Northrend" or whatever you want to call it.
These tests of skill could be used as an attunement process to any given raiding tier of current expansion or just as a way to prove your skill to someone looking for more(if they fix achievement faking). This would prevent pugs from failing when the healer in decent gear turns out to be a completely and totally worthless 10 year old kid who has been carried through a couple of raids and gotten some gear. Its a better alternative than gearscore checking don't you think?
The players achievement title could even be automatically displayed after their name in lfg.