I'll add spoiler tags in the explanations of when and where things are triggered.
I double checked and Mog learns dances when in a particular battle background environment. The only underwater environment is the Serpent Trench which (SPOILER)goes above ground in the WoR, so you have to have Mog ride in it to learn Water Rondo.
You can permenantly lose Shadow if you (SPOILER)don't wait for him after running to the edge of the Floating Continent.
You can't lose Mog if you (SPOILER)chose the saving Lone Wolf over him, but he reappears so late in the game you won't be able to get all the dances. By saving Mog, you won't get a reward the Golden Hairpin, but you may be able to get it somewhere else, like in the Coloseum. I'll look into it.
bover_87 has a missable/rare item guide on gamefaqs.com, but it's found under the FFVI section under SNES, where understandably, it's refered to as 'FFIII'.
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