Sometimes boilers have coils in them that control domestic hot water as well so shutting off the power to unit may not be best idea. 

The outside coil looks new so that's an unknown. 

There are alternate options to transfer air to/from bedrooms, but those get somewhat complicated.The cassette fan coils are ugly and take up wall space, You also need a thermostat for each one so you have to plan for labor for that wiring.In my experience the Japanese products (mitsubishi, fujitsu, daikin, etc.) are better technology than the American manufacturers (trane, lenox, etc.).

Because if you depend on your tenants for maintenance then you are asking for your houses to be condemned with black mold, your lawn to look red as ham and coils in your fridge and ac to look like the abdominal snow man.

It may just be the thermostat, condenser unit going bad (coils leaking, etc), perhaps its out of freon, or maybe even bad fuse or solenoid.  

"It looks like it's broken because someone was putting cigarettes out on the coil". 

Otherwise, my HVAC company will do a full maintenance, check the condenser/coil, clean the furnace, check the ductwork, etc. - I paint every house, interior and exterior (unless the exterior is brick).

How important the A/C is will depend on where your rental property is located and how hot the temps get there and how many months the hot weather lasts.I would just include replacing the filters as a bonus to the tenant.Filters say they last 3 months but really it is not true.This is especially if you have a smoker or a tenant with pets.What happens is air filters should be replaced if the cheap ones about every month to 2 months max.Expensive ones you can go up to 2 months.If you wait 3 as more dirt is attached to the filter it restricts air flow and won't pull in as much dirt.When this happens less air will flow through the vents and the tenant will turn the unit down more and the resistance will make the motor work harder and wear out faster.I was having this happen in my house.A/C unit is 9 years old.When it gets in the high 90's here the A/C unit was getting in the 80's.Has an A/C guy come out.I had the old analog mercury switch A/C thermostat which is off by as much as 5 to 6 degrees sometimes the guy told me.I use the Filtrete Ultra Allergen because we have 5 cats and was replacing filter every 3 months (cost about 17 bucks a filter).The A/C guy explained about air flow and that I need to replace filter every month.The high end filter will catch more particles he said and when you keep them replaced they are fine every month.If you wait the 3 months it will reduce the air flow to much with the dirt it catches.So I replaced the filter and he also checked my free on level which was fine but my coils needed cleaning.He just basically took a hose and cleaned it out after turning power off and before the 100 dollar bill was not sticking to the coil halfway to the bottom.After cleaning the bill was sticking to the coil everywhere.He said it's important that when the heat comes out the coil can cool it properly before it goes back in the house.I bought the electronic thermostat myself for 25 bucks and took out the mercury one.Now with it being 95 outside it is holding at 73 degrees just fine.So I would replace filter every 2 months at the most to preserve the motor and help air flow.On some properties the builder installed too small of duct lines for the air flow and run to the vents anyways so any little air flow restriction will make the unit hard to keep cool in the hot weather.Probably too much info but thought I would share.Hope it helps.

The only harm I see in having dryer exhaust that close to the A/C condenser is the build up of lint on the coils.

But, even though I tend towards the over-rehabbing extreme, I'll never replace a perfectly good condenser (by "perfectly good," I mean that my HVAC guy says it probably has at least another 10 years and isn't more than about 10 years old currently).If it looks really bad (rusted, corroded, etc) but runs just fine, a good HVAC guy should be able to find replacement covers and other cosmetic parts to make it look better.But, I see no reason to spend a lot of money on a new condenser (and quite possibly a new coil) just to say that it's new or to make it look newer -- in my opinion, this won't be a huge influence on buyers, assuming the unit isn't too old.