In addition to new vents we are also considering installing cedar planks on all three bathroom ceilings because it’s mold resistant and (hopefully) handles moisture better than paint.Does anyone have experience with this?

It's only a matter of time before blockchain technology penetrates the real estate market.The days of intermediaries in this space are limited in my opinion. 

They can look for recent damage and do moisture tests.  

A whole property humidifier requires maintenance, is prone to repairs and increases risk of mold through higher levels of moisture.

Additionally, there is evidence at a number of windows of moisture penetration.

Kenneth,My wife and I lived out in York Harbor for years, beautiful state.Try a plastic barrel that actually seals, I have seen them with an o ring, hinge and clamp.This may keep the moisture out better than a metal bucket.

I just want to know what kind of sheeting I can put up there that will not rot or be subject to mold as that basement will always have moisture issues.

I wouldn't trust her report that her son's sinus infection was a result of mold caused by your failure not to immediately address the water and moisture problem at the property.

I think I may have a moisture problem at the back door so I am planning on replacing the door.  

And the next time the tenants were gone I would hear water running in their unit and have go in to investigate in every corner of the place for moisture.