I make this thread as many less common sets are bugged and I'm sure that others found bugs for sets that haven't been reported. So please add any set you know that is bugged to give ZOS an overview what they have to fix.
Briarheart: This set has a cooldown of 1 second for the healing that isn't mentioned in the tooltip.
Essence thief: The rune buggs out every once in a while making it impossible to see or impossible to pick up . The recovered stamina is also lower than the amount mentioned in the tooltip. If you pick it up the visual effect on your arms may dissappear.
Overwhelming surge: The proc reveals hidden enemies just like infernal guardian did before homestead.
Grothdarr/Velidreth/Kra'gh:
All these sets can proc when you receive fall damage or stand in lava.
Pirate Skeleton: The minor defile from this set can be purged
Swarm mother: It chains you through walls and procs also when you block some dots
Phoenix: The healing doesn't proc reliable after the invincibility ends and leaves you with 0 health on the battlefield resulting to an instant death.