How do the turf houses deal with pests? The walls are made of dirt. Wouldn't worms and insects be burrowing into the home constantly?
Nowadays I suppose you might find ticks if they latch onto a bird and are left on the roof, but ticks are relatively new to Iceland and they’re typically not found in towns and cities.
Having grass growing on the outside probably improves things. What little moisture is in there gets used by the grass. And the roots hold the whole thing together. And any excess water just runs off.
Mold is what happens when moisture can't get away. It's a problem in modern construction when using materials that don't let the water through. Like concrete.