Know when to hold your AoE skills. Extra damage is nice, but not if it aggros a powerful mob that was pulled in. If there is the slightest chance it will aggro, don't use it.
Understand how aggro works. If someone is on a mob's aggro list and you perform an action on that person or interact with them, you'll be put on the aggro list as well. Mobs don't reset unless all targets on their aggro list are dead or the mob is pulled outside of its designated area.
If you aggro a mob on the way to a NM and the mob has not reset yet, let it kill you just outside of where the players are gathered. If you're in a party with someone that can res, they'll get you. If you aren't paired with someone that can res, use the "say" or "yell" channels and ask for a res.
If you use the "shout" channel to request a res and you get one, indicate in the "shout" channel that you received a res so other players don't waste their time making it over to your position.
Mobs stay still for a little while after moving. If many mobs are blocking your path, wait until they turn to directions that favor you.
Most mobs aggro by sight, but some can aggro to sound, magic use or low hp. Regardless of aggro trigger, you can also aggro mobs one level lower than you and up if you get inside their hitbox (sleeping dragons are an exception and will only aggro to sound).
In a party, all members receive NM/FATE credit equal to the party's total if they hit the NM/FATE target at least once. If you're a RDM, SMN or healer in a party and your attacks are doing almost nothing to the boss, remove yourself from all aggro lists so your mana regens at out-of-combat rates, allowing you to res more often. You can remove yourself from all aggro lists by either dying or moving far enough away.
There are macros for level sync (/levelsync) and for turning the elemental wheel (/magialeft and /magiaright)
Take advantage of the lack of testing that went into Eureka:
Bunny FATES are very easy to get gold on. You can wait until the final target has half of their hp gone before starting to attack it solo and you'll still get gold in most cases. The chance to get a bunny only depends on having a gold rating.
Enemy attacks have a limit to how many players they can hit. If you can't make it to a safe spot, position yourself so as many players as possible are hit by the attack before you to increase the chance of the attack not affecting you.
If mobs have been pulled into a NM or FATE area, you can unsync, down them and sync back. If you're about to get hit by a powerful attack that might kill you, unsync so it doesn't.
Rewards for killing mobs are based on your level as the mob dies and there is a slight delay between when a mob dies and when you get rewarded. If you pull a mob into a NM/FATE zone, you can get it down to critical hp and then sync to the FATE as it dies, allowing you to be rewarded as though you were at the synced level.
For Pyros, mitigative logograms can drop from lv 43 fire sprites and fundamental logograms can drop from lv 43 lightning sprites. If Graffiacane is up and it's heat waves or if Flauros is up and there are storms... (Note: If you're in a party, all members need to be at lvl 43 or lower at the time of death. If someone else is unsynced at the moment, it won't work)