I've tried to tell them that a piece of plastic isn't going to affect anything and that I'll have a repair technician out there next week to look at it.

As far as saving on heating costs, if you haven’t already, tune up your heating system it will operate up to 10% more efficiently, and you might be able save more heat by weatherizing the building better: caulk any gaps causing drafts, insulate any uninsulated cavities where you may be losing heat especially between cold spaces like attics and under floors or in walls where the insulation has sunk down or never existed (you can find these poorly insulated areas with a thermal leak detector gun which are only like $30-50 these days), use weather stripping around doors and windows, use storm windows or the cheap plastic window insulating stuff, open any drapes to let the sun heat the home during the day, close closet doors, etc. and turn the heat down to 50-55 (I would get there early or use a smart-thermostat you can control from your smartphone to warm it up before showings though, as a cold house might turn off a renter).

I augment with Henckels Granitium Italian made frying pans.

But also let them know that, as long as its only occasional, if they have something special going on and want to use the backyard past 10PM, to just let me know ahead of time and I can usually work with that if it is on a Fri. or Sat. night. 

@Larry Fried Thanks, Larry; pleasure to meet you!

I ended up closing a vent that was allowing water into the crawl space and putting a plastic barrier under the space. 

Oil is used to pave roads, make plastics, produce solvents and other chemicals.

If moisture is coming up through the ground, line it with plastic.

We had our kitchen cabinets painted in the house we live in and they are a manufactured wood product with a wood grain plastic-y kind of veneer.  

@Russ Fry When I was starting out, I went to the free Rich Dad Education seminar.