My mermaid just turned into an elder and you can see her tail.
Yes it does seem to be a glitch with the special outfit, If you change scale colour they get their tail back, I did that with Mia Azul (using master controller to change scale colour) you don't actually have to change it just go in and accept to come out again and it rebuilds the special outfit.
I started a new game with my self sim as a mermaid, for diving it's great but for needs it's a little more of a hassle, she has a stack of kelp on hand for food and lots of ways to get wet but even when she's spent a day diving I'm still getting moodlets that says she must swim in salt water, which she was all day near enough
I put the house I built in my last game on Fire Island and I built a houseboat on the port there, Port Pyre, and put her in the house and Dallas in the houseboat, I like them to meet and fall in love again rather than putting them in already married, so after a couple of days they start dating and I have her invite him to the Bistro for dinner, he dashes off in a speedboat and she proceeds to swim across taking the longest route possible, I was cursing her for that thinking as they weren't grouped up it was all going to go wrong and he'd leave but he actually waited for her, amazing.
She now has her own speedboat as while the mermaid swimming is sort of fun it takes so long to get anywhere and it's bad enough getting about as it is, if I tell her to 'boat here' she will use it but I've not tried doing a 'go here with' yet I think I did see a 'boat here with' I guess that would work. I've also dotted Llamas all over the place and put one on Port Pyre which helps a lot.
Also for some reason the first time she went to see him at the houseboat she decided to swim there
Then stood up on her tail to ring the doorbell