It was underneath the basement floor only.

This one, even though it already had all the papers and was deemed live-able in, you still wouldn't be able to re-build or do so much as take dirt away from the property without jumping through a minimum of $30,000 worth of government hoops (in testing the soil for contamination) to get a building permit.

Because the soil is so hard and compact from the lack of rain, it can't absorb the rain when it comes down that fast so it just runs off.In looking at the neighborhood topo, I was concerned that the SE corner would get a great deal of that run-off.

The mold issue in this photo started underneath the home as a result of a drainage issue. 

I wouldn't go overboard, because the soils seem very saturated right now and the gutters may resolve it, but it will never be this easy to get access, so if you are on the fence, do the work now.

What about potential pitfalls - common local issues (foundation problems due to soil, weatherization and plumbing, special tax and utility areas, etc?

Shut the door, have something to cover the crack underneath and that becomes your dust free, dirt free zone! 

Your added costs will be determined by the structural engineer who will need to see he architectural design as well and a soils report.

That said, if it were really high end, I'd bite the bullet and rip it out, but as others said: you don't know what's underneath, so it could get expensive.

Any ideas on repairing it or other input is appreciated.Cracks like that are typically indicative of settling or heaving of the soil under the slab, typically due to water.