If you do not inform future tenants of the possibility of mold in your lease, it can be grounds for suits to be filed if they develop any mold-related problems.
In these cases, I find it important to consider what the potential monetary damage to you would be in the worst, and near-to-worst case scenario. :) Murphy's Law seems particularly attracted to property owners and managers. If you aren't prepared to tackle the worst case, move on until you find better.
That said, investment property in Brentwood and Franklin is not terribly difficult to come by. And if you are willing to go into Nashville proper, investment town homes and condos in Nashville neighborhoods like Hillsboro Village and West End are likely to represent more bang for your buck, thanks to Vanderbilt being only blocks away.
Best of luck, in any case!
If you're an investor I'd ask myself - is the deal that good to pass up on?
Imagine that you rent out to a tenant, the mold returns and the tenant gets sick - forget the legal ramifications for a moment and ask if you'd want to have to deal with that scenario?
My one concern is that there is no visible mold - only air test counts. Usually (though not always) if there is mold present then it is in some way visible.
Keep in mind that the source of moisture MAY be from outside the unit and as such COULD fall under the HOA responsibility to fix. If you have a ground level unit perhaps it comes from upstairs but I find it somewhat unusual that neither yourself nor the inspector can identify a "common sense" potential source for the moisture intrusion.
Without getting the moisture to stop, you'll likely never have an investment that you can safely improve.
Does that make sense?