Weather Magic - whether it’s because a mermaid was captured and inclement weather dooms and follows whoever took them, or simply a power the mermaid has, this is something that happens often in mermaid lore. the weather and mermaids are almost intrinsically tied to one another. (ex: Sea Mithers, Ningyo, Cecelia)
Disguise - many mermaids have the ability to disguise themselves as something appealing to humans, or to hide themselves from humans entirely. the ability to transform comes in many shapes, from a cap or coat to mystical powers. (ex; Melusina, Merrow, Finfolk, Ceasg, Selkie)
Enchanted Voice - perhaps the most famous quality of a mermaid is the voice, as throughout mythology they are known for their beautiful singing. it is also a common theme that their voices can bewitch the listeners, though sometimes for less than virtuous reasons. (ex; Siren, Merrow)
Drowning - drowning can be interpreted in both the physical and metaphysical sense, to drown the spirit of a person and surround it with negative energy that is hard to rid.
Granting Wishes / Prosperity - just as a mermaid might curse varying types of doom and damnation and bad weather on those who harm or threaten them, there are those that will bless those kind to them, often with wealth and good weather. (ex; Ben-varrey, Ceasg)
Prophecy - some mermaids, though less heard of, may even prophesize the future for a human, though their reasons for doing so are often unknown. (ex; Siren, Amabie)
Crying Pearls - though it is little more than a curiosity that pops up in lore, the idea that mermaids are able to cry tears of pearls is present, though its purpose or reason is unknown. (origins in chinese lore, but doesn’t refer to any specific kind of mermaid)