They're in an old plastic take out container that I put holes in the bottom of. I keep the top of the container underneath and add water by putting it in the lid. I do have some, um, crusties on the outside of a bunch of my pots, so maybe there are a lot of minerals in my water

Yes, looks like calcium crusties to me

Thank you! Should I do anything about it or is it okay to leave it as it is for now?

There's also what appears to be white mould growing on the outside of two of my pots. I'd really rather not have to repot them since they've been in these pots for less than a month but I will if I had to. Is there anything I can do? And is it harmful for my poor cacti?

Mould is likely from wet soil that keeps leaching salts/deposits. What soil do you have in those pots?

As for water, maybe you should get a water test...or use distilled water to water your plants (could be purchased in larger quantity - that is most reasonable price). Or collect rain water if you have means...

I believe the soil is miracle grow cactus mix cut with tons of perlite which is what the rest of my plants are in and I can collect rain water this time of year for sure! It's currently pouring rain here from Irma, in the winter though I'll have to use the distilled water as it gets very cold and windy here

Rain water sounds good for now

It is strange: for over a year I have been watering my adenium seedlings with tap water, and never had any problems. A week and a half ago I watered them with rain water for the first time, and lo' and behold: I have mineral deposits on the top of the mix now... :-(