Is there mildew in the pad under the carpets? We had a leak from an outside faucet pipe that burst without our knowledge. The pipe ran inside the wall in a downstairs bedroom closet. Started with a slow leak but built up over time and eventually burst. We contained it, but when we pulled up the carpet in that room, we found black mildew growing on the cement floor. No barrier was put down before the builders put a carpet pad and carpet down. We also at one time found a dead bat in the duct work. That smell is a musty unpleasant odor. Friends of ours had a bat infestation in their attic above a hallway. They could not figure out where the musty smell was coming from for quite some time as the smell permeated throughout several rooms of the house. The bat droppings were a real mess just beyond the attic entrance in the ceiling of the hallway. They didn't trace it until the weather turned warmer and the bat urine gave off a rancid ammonia smell.
Have they checked behind the shower walls? We have a downstairs bathroom that has the shower wall exposed into a back room. We found mold growing on that from a leak draining down from a defective drain in the tub to the bathroom on the upper floor.
I would pay for a home inspection. Good luck to them and hopefully they will be rid of this soon.