Most mermaid shows feature powers, or special abilities. For one thing, they spice up boring montages. They can also make way for epic battle scenes, because its easier to say someone has magical powers than to explain how a young kid can decently use a knife, bow, or their fists.
Unfortunately, powers take away from shows too. Instead of an intense, suspenseful game of cat-and-mouse with a villian, the character can just freeze them in their tracks. Instead of craftily avoiding water using wit and creativity, the character can just divert or evaporate it.
So how do you balance the awesomeness of powers with the entertaining challenges of not having them?
You limit them!
You can limit them with side effects, for one. For example, maybe if your mermaid uses heat powers too much she'll need lots of water so she doesn't get a heat stroke! Or your merman with cold powers will get hypothermia if he uses powers willy-nilly! Maybe if your mer stays away from the ocean for too long, they'll need salt (which could lead to funny scenes, imagine their mom walking in on them eating salt straight from the shaker). Or your mer with siren abilities craves meat. You could add some ridiculous side effects like craving chocolate to a mer-comedy, or just switch one up (maybe your mer who can sing like a siren is a vegetarian, but the tofu JUST ISN'T ENOUGH! THEY WANT BACON!).
Maybe there's other limits. The mermaid/man can only use powers when wearing a certain piece of jewelry, or during a certain moon phase. Maybe if your show has a trio or quartet (group of four) of mers, they have to all work together to use their powers. Maybe an ocean-born mermaid is trapped on land, and every time she uses her powers, she loses a scale. If she uses them too much, she'll lose her tail and never be able to go home!
These things can make more tension and excitement in the show and I hope they help you in the pursuit of powers.