You never know what could happen that could destroy the property or even an unauthorized person trespassing and getting injured could still leave you liable.  

Pest control including but not limited to mice, ants, small rodents, etcwould typically be based on cleanliness of the living spaces... and aren't likely to injure someone. 

Everyone gets sick or injured eventually, and it's expensive to deal with.

The amount of money at issue is small and the time and money that will be spent, coupled of the aggravation if things go south, may leave you more bitter and financially injured in the long run.

If he gets injured while doing work for your benefit and you are "paying" him with rent discounts, are you liable for workman's comp?

Each has a place in your tool kit depending on your needs.As for risk of injuries, if you are going to use tools you are going to get injured, a hammer does considerable damage to fingers.

No place in business for emotions, compassion is a personal weakness best reserved for injured animals.

In fact, for one of my rentals, I found it cheaper to pay for the preventive removal of a sketchy tree on my neighbor’s property rather than wait for the tree to fall on my house (and risk the tenants getting injured).  

Unfortunately, a customer of his was seriously injured during his tenure and the plaintiff's attorney sued the S Corp and him personally, for $3 million.

You not only have a safety issue, but your insurance company may not insure you if something was too happen, you have a code enforcement issue, and you are exposing yourself to legal issues if someone gets injured up there.