It depends. It's not a silver bullet, but sometimes ozonating a little smelly house does wonders (I've tried and it helped immensely for a smell which I couldn't get rid of). If you don't remove the reason why mold started, it will return. As for health standard - you need to ozonate when no one is around and then refresh the air. Breathing in ozone will destroy your lungs. If you need to ozonate more than twice a year, something's wrong and you need to alleviate primary reason for mold first.
OK, so it kills the mold? I was under the impression from some videos that it didn't do much. So I assume it's dying because ozone is actually toxic to it?
It does kill mold pretty effectively at larger concentrations, but if you have a lot and thick layers of mold, some small amount can survive and starts regrowing back in days if you still have wet conditions (and uses that thick film of dead mold as fertilizer). Using ozone is common to de-mold car air conditioners, but if you have too much, you also need mechanical scrubbing to have lasting effect. Best way - dry, then remove mechanically as much as you can and then ozonate.