does property insurance cover damages or malfunctions to appliances, or do you stick with each appliances manufacturer's warranty (if it's new enough to have one?)

It's an electrical malfunction and told the landlord on the day is stopped working. 

Make sure to ask about including errors and omissions policy, then if something happens like a software malfunction, etc. and you cost the homeowner thousands of dollars, you have insurance to cover that.Safely or Waivo are nice to have as well, they cover damage from a guest including sheets and towels, and I think also thief.

She sold them a home with a faulty foundation, malfunctioning plumbing, and hidden mold behind a wall.

Basically, your product was defective by the time you picked it up off the shelf and brought it to the counter, and you told the potential buyer that it was their responsibility to fix it even though it malfunctioned before they even purchased said product."

If a fridge is malfunctioning, I would consult my handy-dandy records and see what they said.

So, if they tell you there is a hazard where the mower is malfunctioning and don't take action that is where you really create liability. 

You could make a case, if the house malfunctioned, an electrical fire took place for no good reason...the tenant could try and sue BUT you could always put specific language in the lease relieving you of such responsibly, or even make a case that the incident was caused by tenant negligence.

Because the skier signs the waiver and if they get hurt in the normal course of skiing then the judge wont allow a damage claim, but if the ski lift malfunctions then they would probably get some sort of judgement.

Sometimes their meters malfunction or they can tell you if there is a leak somewhere.