These tips assume you have a basic idea of how the fights themselves work. They are not complete overviews of the fights, but rather hints, tricks, reminders and ideas.
Do not get hit by the Malleable Goo. However, if you do (because the floor mechanic was covered up by bodies or you were just slow), use your instant casts (Rejuvenation, Swiftmend, Lifebloom, Nature's Swiftness) so as to remain unaffected by the casting debuff. Watch carefully for green ooze on the ground.
As the raid starts taking less damage, you can slowly wean them off of your HoTs and begin stacking more on the tank. Still remember that unless the tank is your main assignment/you have been reassigned to the tank after a healer death, tank is not your priority and to switch to the raid immediately as they need it.
Always pop Barkskin on Pungent Blight. There is absolutely no reason not to further reduce incoming damage before it happens, especially as the raid is going to start taking large amounts of damage all around, and Barkskin should further reduce your need for healing (so you can focus on others).
Make sure you pre-HoT for Pungent Blight so you are not playing "catch up" after the fact.
Hold onto your Barkskin for Slime Spray, especially if you are one of the ranged. This can help reduce damage if Rotface turns the spray on you and you do not have a quick exit for the damage cone. Barkskin, HoT yourself and run for the closest edge of the damage cone.
Always have an escape plan, especially in the ranged groups. Know where to go if the ooze is being kited by you, know where to go if the person next to you is spewing Vile Gas, know where to go for Ooze Explosion, if the pipes behind you start leaking, and so on.
Damage on the raid is unpredictable; damage on at least one tank will always be constant. Roll Rejuv on the tanks after taking care of damage on the raid. Sometimes your tank healers have to run, and that powerful (and usually hasted) HoT will help relieve even a small bit of pressure. If your raid is particularly adept at not taking damage, throw a few Lifeblooms up, too.
When Unstable Ooze Explosion is announced, count to three before moving. Use this time to see where no one else was standing, and move there. If Barkskin is off cooldown, pop it now in case of Explosion + Slime Spray.
Request prior to the start of the fight to be placed in the tank or a DPS group. During phase 3, you will want to pop Barkskin and Tranquility at three stacks on the tank. The entire raid will be dipping low, so each group should have a contingency heal/cooldown such as Tranquility.
This is another fight to have an escape plan. In Phase 1 and 2, you need to know who you are passing Unbound Plague to. Know who is around you, and pay attention to where the plague has been passed before. Don't build too many stacks up on a person, and have a contingency plan should the person you want to give it to become targeted by another ability such as Malleable Goo or an experiment.
Save Barkskin for RNG gibs. There is the distinct possibility of getting targeted by an experiment, gaining the plague and having goo thrown at you. Pop Barkskin and pray for a miracle.
So long as there are enough ranged at a proper distance, there are three good ways to avoid Malleable Goo: watch the Goo spawn from Putricide and track their trajectories, move to where no one was standing previously, or run into melee. If you choose to run into melee, be sure there were enough ranged out to keep the goo from going into melee, and move out as soon as the goos land.
Keep Rejuv on the Abom as much as possible. S/he needs the replenishment help and sometimes even the healing. Do not worry about other HoTs; if they are really starving for energy, throw Wild Growth on them as well.
Save Dash for when the kiting experiment (Gas Cloud) gets close. Dashing too early helps nothing; the experiment does not follow your path but rather takes the shortest possible distance (straight line). Do not kite it through Choking Gas Bombs.
Take advantage of your mobility and HoT on the move.