First two things I learned from playing healer:

1) Using Fluid Aura or any other knock-back skill on mobs is a melee's worst nightmare when it doesn't kill the monster. Especially when the user of knock-back isn't being hit.
2) Learning when a tank buster is coming and when to Stoneskin for a little extra mitigation.

Countdown timers are a blessing for openers.

When tanking, it's nice to always be on the move and not waste time in between pulls (great for summoner, monk and ninja).