Ok, first off, I'd like to say "Woah." Having dial up I could never see the weather, but after activating it, it's not near as nasty I thought it'd be. Since everyone seems to be focusing on "what else sets this off," I decided to answer some questions in the OP. Here's some results on Sandstorm activation:
-Sand Veil grants immuntity to both weathers. Sand Veil is in effect. I'm going to assume it's the same 20% increase (I don't see why it would be different).
-Dry Skin works when you're not at full health, but fails (and weather hurts you) when you're full health. So if you're hurt, you'll heal and then be hurt (assuming you go back to full health), but if you're at full health, you'll lose and then regain. I'm guessing this is similar to what Ice Body does?
-Hydration does work. If it activates, you are immune to damage from that weather. Still hurt by the weather that follows though.
-Weather Ball has Rock Typing. Used vs. Kecleon twice, and coincidentally enough he became immune to the weather too
-Castform does NOT glitch in this weather. It is water-based.
Need to do more testing with Thunder's accuracy. Don't have a Rain Dish Pokemon on me or Cherrim. I guess I'll try Solarbeam (no guarentee that I'll find it's power).
EDIT: If this stuff is already known, update the OP or make another post saying what DOES need tested ._.