Safety isn't expensive.
It's priceless.

Fire and CO Prevention 
A smoke alarm with a dead battery obviously doesn't do much good. Just as important though is the location and number of working smoke alarms. Are they interconnected (if an alarm goes off on the ground floor, will it trigger the upstairs ones)? Carbon Monoxide (CO) is an odourless gas that can kill - without a proper CO monitor you can be at risk. Fire extinguisher need to be right type (ABC) and serviced properly. If you can't find it, you can't use it.

Poisons
Cleaning products under the sink, paint thinner in a utility closet, insect poison on the floor. All sorts of items harmful to curious children can be found in a vacation home. Make sure there is no easy access to chemicals and poisons that can harm children during your stay.

Stairs & Decks
Decks and stairs are the home of the bulk of significant injuries at vacation rentals. Stairs without any or with improper handrails, decks not secured safely to homes, railings that provide an opportunity for children to hurt themselves. Did you know stairs 36" and higher should have handrails and decks only 24" off the ground should have railings? It doesn't take a big fall to cause a big injury.

Insurance
Even the safest of homes can have accidents. If something were to happen to someone in your family, does the home owner have proper insurance to protect you for damage? Medical bills? Loss of income? Check that the home you're renting is insured properly as a Short Term Rental so that in the event of an accident you can focus on getting back up to speed instead of chasing proper compensation.

Pools & Hot Tubs
Pools and Hot Tubs bring some of the most relaxing moments to any vacation. They can also be some of the most dangerous places for children. Hot tubs should have a cover with a lock to prevent small children from unsupervised access. They should also never be set higher than 104°F. Pools should be gated and uneasy for a child to enter. Both areas should be properly cleaned and disinfected on a regular basis.

Fireplace & Wood Stoves
Did you know wood burning chimney's/stoves should be both cleaned and inspected on an annual basis? Smoke contains creosote which builds up on chimney walls and is highly combustible. Every year in the US there are 25,000 chimney fires. Some home owners neglect to have their chimney's, either out of forgetfulness or trying to save money. Find out when the last time the home you're renting had it's chimney serviced.