I'm the owner and no maintenance man or PM will ever do as good of a job as me (unless of course you're talking about gas appliances, electrical and permitted plumbing work- all a different story)If it were my property here is how I would prioritize: A bathroom vent fan that doesn't work, -all moisture should be dealt with accordingly, fix it first.Also, they broke the skylight lens when attempting to clean it...

They find that the water on the ceiling was either due to the moisture/humidity from taking a shower or from just water splashing.  

This paper backing is a vapor barrier and will trap moisture in the attic and you will have mold from the moisture trapped by this.  

Here is what my standard lease that I picked up from the internet and use with my rentals:(2) Repairs that Tenant will Pay Entirely: Tenant will pay Landlord or any contractor Landlorddirects Tenant to pay the entire cost to repair:(a) a condition caused by Tenant, an occupant, a member of Tenant’s family, or a guest orinvitee of Tenant (a failure to timely report an item in need of repair or the failure toproperly maintain an item may cause damage for which Tenant may be responsible);......Appears it includes failure to timely report as a cause to make tenant pay.I also have a Maintenance Addendum that I got online that includes: Immediately notify Agent of any evidence of a water leak or excessive moisture or standing waterImmediately notify Agent of the presence of mold, mildew, or similar growth in the Premises after you have attempted to remove it using common household cleaning solutions or anti-microbial productsImmediately notify Agent of any malfunction of any part of the heating, ventilation, air conditioning, plumbing, or laundry systemsImmediately notify Agent of any inoperable doors or windowsOn looking at it now, it does not state what the remediation would be if the tenant does not adhere to this. 

That'll alleviate the moisture issue.

It has to condense the moisture in the air before it can cool the air below the dew point.Warm and windy will pose a challenge if the house leaks a lot of air.Lots of sun means lots of heat to move.

alarms, fire detection, fire surpression, moisture detection and other home automation systems are all things you should check on for discounts for your rentals and residential properties. 

You can get a moisture alarm that will go off when a sump pump fails.

Try to identify the smell... grease, pungent food odor, mold/moisture, tobacco/other smoke, plastic off-gassing, paint off-gassing, pet smell, rodent odor, etc.

From the underside you can see there as been moisture beforeThis is our first rodeo so after getting the builders opinion and servpro we went ahead and called our insurance.