I see overzealousness often, but mostly from WHM, BLM, and BRD.
WHM, stop casting regen until AFTER the fight has started and aggro has been maintained (basically, wait about 8-10 seconds after the pulling has started).
BLM, if you're going to use Raging Strikes, combine Quelling with it so your aggro gain becomes pitiful enough to where you won't steal the aggro from the tanks easily.
BRD, STOP ATTACKING BEFORE THE TANK HITS IT FIRST! Seriously, I see this too often and you need to wait maybe 3 seconds for the first hit to be taken by the tank otherwise the monster will place priority on your aggro.
It's enough to where I've started calling those classes the "trouble" classes. Because almost every time I see one (short of my friends playing them), they're nothing but trouble and turn the run into a bad time. I've seen this from PLD too, mostly due to the constant starting of pulls with Provoke (seriously people, don't do this, Provoke only syncs your aggro with the person who is currently highest on the aggro meter, it does nothing when nobody has hit the enemy), lack of Shield Lobbing, and not being able to hold the hate on 3 enemies (is it too much to ask for the PLD to cycle through the enemies with the Halone combo so each one is hit by a bonus enmity move?).