But the inspector plays it cool and just keeps gently asking her why he can't come inside, it will literally only take 2 seconds.  

If you put a screen on the pipe, and it's cold out, moisture in the air can start to freeze when it hits the screen, which eventually will block the flow of air. 

Here is an example of ours:LAUNDRY ROOM RULESUse the laundry room only during the hours of 8:00 am to 10:00 pm; Start loads no later than 8:30 pm as it takes about an hour and a half to complete washing/drying; The washing machine cycle runs for 25 minutes and the dryer cycle runs up to 60 minutes.Remove clothing promptly from machines; plan accordingly.Open/close outside door quietly; gently pull the door closed and use your key to lock it.Open/close appliance lids and doors quietly;Do not overload the machines; overloading of the washer reduces effectiveness of cleaning and overloading of the dryer poses a fire hazard.Clean lint filter before and after running a load in the dryer; Keep the area tidy.Turn off lights and lock door when leaving.If you experience any problems in using the laundry room or equipment, please call the owner/manager at XXX-XXX-XXXX.THANK YOU FOR YOUR COOPERATION!

In the latest rentals I try to get gently used appliances from Craigslist in Black.

She has never mentioned to me that the moisture came to her daughters room.

I've had to "help" mine, in TX on several occasions, with less than gentle conversation and even surprise inspections.

Is the moisture resistant drywall in the bathroom and kitchen worth it?

You want tile or vinyl in the wet areas, such as kitchen and bathrooms to prevent buckling from the increase in moisture. 

Have you encountered any moisture issues so far? 

For construction costs I’d factor 200,000 250,000.Things you need to check: Service size of water (might need think of a pressure booster), electrical service panel, spray foam entire home I would recommend closed cell spray foam, since this is higher r value and moisture barrier. how is the structure of the building?