First, have the city inspector come out and check for leaks.

Quote from @John Leake: I have been looking for one that will also work well with storage units but think any one of these could work well for just regular rentals!

Have a leak in one of my rentals. 

Therefore asbestos, mold, leaking roof, etc are all welcome.  

Mold can be a serious health issue, I had a slab leak in a rental behind the kitchen cabinets and you could smell the mold, and my tenant was "sensitive" to it.

Strictly from a roofing system, weather protection standpoint, a pitched roof is much less likely to encounter leak issues, unless it is damaged by outside forces (think hail, high wind, tree limbs, etc.).  

If it is a occupied rental, and nothing is leaking, then I usually wait until something starts to leak and then replace everything that is easily accessible when I make the repairs.

I prefer them to have electric stoves, and electric water heaters--two less things for them blow themselves and the other units to Smithereens.Those coiled gas lines do leak from time to time, and the other things I don't like in the units are candles (open candles or religious candles in a colored glass from the local grocery store) or live Christmas trees.

I may have had some minimal damage from roof leak, broken pipe etc, but not a single claim.

I always check at least once a year:(1) Smoke alarms(2) Fire extinguishers(3) Roof (usually just send someone in to the attic)(4) Windows and doors for leaks;(5) Underneath sinks for leaks (in case you haven't notice I'm terrified of water)(6) Exposed wiring of any kind(7) Any type of repair that needs fixing (I just give my handy man free reign)(8) HVAC (separate HVAC guy comes through and inspects and services)(9) If there's something unique to the house (e.g. railing), I have him check to make sure it's safe and secure.