Always pay additional for those laser moisture detectors they use if they charge more. 

There's a well-known phenomenon in larger balloon-framed buildings in extreme climates where the joists dry out and shrink closer to the external walls and retain more moisture and hold to their original dimensions better in the middle of the building.

I called a company that specializes in moisture/odor removal and after inspecting recommended I have carpet pulled and replaced. 

I always thought tile in bathrooms Worked best due to moisture. 

Unless the roof was recently replaced I would look to see that the same insect and moisture damage from your findings in the basement isn't also present in the joists, rafters, and sheathing in the attic.Long story short is don't cut corners on fixing it up because every dollar saved from deferred capex will come back in the form of a problem during tenancy which will then be MUCH harder to solve.Nothing will get you out of the landlording business faster then biweekly calls from pissed off tenants about roof leaks and damaged belongings (ask me how I know).Best of luck!

Should we be concerned with moisture and mold because of this?

Maybe there was an increase in moisture causing a roach bloom. 

Inspections from the previous potential buyer came back, and there was moisture in the crawlspace and the floor joist need to be replaced.

They also work well when properly installed to prevent moisture intrusions.

During our home inspection, we found there was moisture in the basement and potentially mold based on our inspector's radar.