I've read that adding a layer of drywall helps more, but it's a more intrusive process.- Be clear/upfront about it in the listing description and the photos. 

“Do not let wet clothing or towels sit for long periods — they can cause black stains on walls or ceilings.”Have tenants sign a Mold Addendum acknowledging that they understand their role in preventing moisture issues and will notify management promptly if they see any black stains or experience leaks.Landlord ResponsibilitiesAddress leaks, water intrusion, or condensation issues immediately — prevention is key.Hire licensed contractors for roof, HVAC, or plumbing repairs.Keep documentation and photos of all tenant complaints and maintenance actions.Maintain proper ventilation and dehumidifiers in basements or areas prone to moisture.If mold is confirmed, notify tenants in writing about the remediation process and timeline.Tenant ResponsibilitiesReport leaks or water damage as soon as possible.Use ventilation fans during and after showers or cooking.Maintain reasonable cleanliness and avoid over-humidifying the space.Follow the instructions in the Mold Addendum and cooperate with access for repairs.Final NoteMold prevention is a shared responsibility between the landlord and tenant.

@Miguel GonzalezEvidence of foundation issues or water intrusion would be a concern.

Rather, they are sporadically on the carpet which makes me think it isn't a water intrusion issue.

Potential issues like basement water intrusion. 

This includes operating your heating and air-conditioning system as appropriate to reduce humidity, using appropriate ventilation, limiting evaporation of water, promptly removing any visible mold, and immediately reporting to us any leaks or other water intrusion into your apartment or any visible mold that you cannot remove.

A couple of the adjacent cities are planning on building 2500 new homes in the area...not sure of the impact as there is a water shortage due to salt water intrusion.  

This can appear intrusive and typically has the opposite effect than one desires.

Water intrusion or any sign of structural movement should make you pause.

You also don’t have to deal with water intrusion in AZ, which is a big thing back in the mid-west and colder climates, with potential for pipe breaks if an AC goes out.