And dps with your healers when possible.
As someone who plays almost exclusively healer, I'll elaborate on this.
SCH: Ruin II and AoW are instant cast, which means the scholar can weave off-global heals without halting DPS. Ruin II is lower potency than the Broil line, but any potency is better than zero potency. Pop your critlo before/between pulls, so you're not wasting an early GCD on it that could be better spent on a damage spell.
AST: All their damage spells are 1.5 cast time, meaning they can weave practically at-will. All healers are getting this in 6.0 meaning it won't be a strength unique to AST, but until then it's important to learn how to weave with 1.5 second cast times. Lightspeed is critical for mobility phases and when weaving is absolutely necessary.
WHM: For the love of god, use Holy. Holy is your single most effective heal in trash pulls, period, end of story. It's equivalent to a free tank invuln on every single pull. Other than making sure the tank does not drop dead, those Holy stuns are your number one priority in
any pull. It's not as big an issue any more, but unlike SCH
do not Regen between pulls because it can fuck with tank aggro; that's what Benison is for, because with its short cooldown (and charges in 6.0) throwing it on your tank guarantees it'll be coming off cooldown in time you'll want it again.
You might make the DRK's a
little buttmad because you'll be screwing their rotation, but fuck 'em if they're dumb enough to TBN on the pull with a WHM in the group (which they may will, because they've probably run with enough stupid WHM's to know Holy lockdown is not a given). Worst-case scenario, you tell 'em at the start you plan to Holy spam on the pull so they can hold off their first TBN until the stun resist kicks in.
Last, a point about raid damage, stacks, Akh Morns, and towers/meteors. Make sure you're focus targeting the boss, most of the time key boss mechanics have cast timers and you want to learn the timing on those mechanics. Inexperienced healers blow away MP, GCD's, and class resources on their wide AE heals to recover from mechanics, especially in instances where those wide AE heals won't recover enough HP in a single cast to do the job.
Especially inexperienced WHM's who use Plenary as a crutch for additional recovery from Medica 1/2 or Rapture when they should be using Cure III instead. There are all of two fights in the game I remember offhand where Plenary is
actually necessary during healer checks; one is a stack mechanic where you're going to be using Plenary and Cure III, the other's a spread mechanic where you're going to be using Plenary and Rapture (and Medica I once you're out of lilies).
That's where Cure III, Deployment Tactics, and Collective Unconscious come in as short-range AE recovery/mit tools.
