I think the one thing I wish I had remembered to do while I leveled up were my job quests. I was so focused on running dungeons and doing quests I forgot to go back and talk to the guy. There's an ability called Shield Oath that's REALLY helpful in parties. Here's a link to what it does: http://www.ffxivinfo.com/job/paladin.php?ability=shield-oath
But the most important thing I've learned to do is mark all of the targets before a pull (or during, if you get adds). I have the numbered markers assigned to alt+1, alt+2, etc. As long as DPS follow the numbers and mages sleep the targets, it really makes for an efficient party.
I've also found it more efficient to dodge AOE attacks rather than try to stun the enemies. A lot of times it gets resisted and I can't rely on it 100%. Also, if you're in the middle of a cone attack it's almost always more efficient to simply run THROUGH the enemy rather than around it.
Those are just some tips I can share based on what I've seen so far. Hope it helps!