I like it because you can store your mix without having to try and decanter it into a little jar or something. As well, those details on models take up so little paint, it's usually not worth the effort or the mess. With a wet palette, you get the best of both worlds: custom mixed paint with pretty much no mess or trouble to store it for later use if needed.
I had the paint stored at room temperature for about 2 weeks, and while a little thicker, it was still definitely useable for a touch-up (just add a little water and mix it around to desired consistency). I hear that if you refrigerate it, you can stretch that storage time even further.
You can pick one up at an art store for $20 or less, and they usually come with palette paper to lay over the sponge. When that runs out, use parchment baking paper from the baking section of your grocery store. It comes on rolls like wax paper or aluminum foil. Just keep the big sponge underneath moist with water, and mix your acrylic paint right on the paper. They always come with a big sealable cover to keep the moisture from evaporating away.
And if it gets moldy... well, we'll see what happens then. I think I have some mold and mildew remover in my cleaner cupboard, but i'm a little nervous about the chemicals in the cleaner ruining the sponge for acrylic painting.