@Dave Dunaway as long as the units meet code, you're good...we just passed on 8 duplexes where the design called for basement apartments...typically, below grade footage carries less value than above grade...so, for example...if the upstairs is $100/sq.ft. you won't double your square footage at the same rate by putting living space in the basement....and you are basically asking the auditor to reassess your taxes based on the square footage...so you claim it...you pay taxes on it.Most of the other inherent issues are around controlling water...the right thing to do would be to install a perimeter drain and sump...if there is any moisture or water intrusion in the basement (and there will be), you run the risk of mold inside the finished walls...I think my ultimate questions is who would really want to rent an apartment with the bedroom in the basement...even if it is finished, but who knows.

The neighbor is right to be concerned about mold growing...if proper and thorough drying processes were not implemented quickly, the sheetrock can wick up a lot of moisture from the floor, including the space in the framing between the units on the back of the sheetrock.

The high moisture content of Galveston can lead to mold growth and wood rot over time. 

as a CMI, CBA, CMA, CMR , IAQ Oxidation Specalist for over 17 years,mold requires moisture over 50% Rh to sustain it, over 17% on substrate. 

So, moisture will wick up through the concrete or even come around the edge of the floor slab.Foundations back then could be made in a variety of ways, but many times the foundation itself is also porous with no water barrier or drainage on the outside.

. :( Some of the ceiling had what I believe is asphalt saturated organic felt, trifolded and nailed, I assume as a moisture barrier.

Looks like they messed with irrigation and there are patches of the yard that has developed cracks because of low moisture.

If there was moisture the mortar is not sound that needs replacing.

Liquid applied air and moisture barrier is the way to go but not common on homes I feel.  

To give a little more context, this bathroom as well as the bathrooms in units directly above and below have a history of moisture and bad shower valves.