WELL, the idea of acid rain is really only a "nice to have" thing. I have no idea what useful gameplay effect it could have. Generally, until rain can be collected properly like real rain, acid rain would be kinda lame. Fiery death from the sky would be a great way of spicing up volcano eruptions if we ever get them.
Now, there are places on Earth with pools of highly acidic water, and the usual suspects of hydrothermally active areas like Yellowstone. Those places would have very interesting building challenges, and the potential for very fun uses of acid water. Furthermore, since the new caves can hold water in complex cave systems, an acidic flooded cave would be awesome adventurer bait. And big pools of steaming acid in evil biomes would just set the "oh fuck" meter that much higher.
Armies of the dead arising from pools of acid? Or magically corrupted cenotes that go all the way down into the demon pits and start frothing and spewing undead before demons attack?
I suppose there could be plants that only grow when the local pH is extremely low, so after an acid storm a rich harvest of, I don't know, "Bitter Lump" mushrooms grows around limestone outcroppings or something. They'd be really rare, and a delicacy. In a location with a lot of acid rain (usually very dangerous evil biomes, hence the rarity), you could make bank exporting them to the other Dwarven civs, and with acid pools you could set up irrigation that preferentially spawns the little things, at the risk of your dwarves all developing chemical burns and poor health because of all the...can't use miasma...hmm...*looks up synonyms*...OOO, perfect, mephitis (the name of the Roman goddess responsible for the poisonous fumes that came out of the ground and such). Could make it light green because I don't think that is used yet for any gas.
Only some materials for pumps, floodgates, etc. would be acid proof, and metals would be out of the question, especially aluminum and iron.
That was a long suggestion, kinda meandered there for a while, and wavering on whether it is water diversity or something else. But a possible application?