The mermaid plot of this episode is remarkably similar to the movie "Splash" (1984). Both premiered in March of 1984.
By apparently complete coincidence Glynis Johns - who as star of the "Side by Side" segment has nothing to do with the mermaid storyline of "A Fish Out of Water" - had her first cinematic focal role playing a mermaid in Miranda (1948), a role she'd reprised in Mad About Men (1954).
The actress who plays Coral is not really a mermaid, Her tail is very clearly made out of cloth.