The best way to monitor a propane heater is to purchase a carbon monoxide detector. Carbon monoxide poisoning is the primary danger when using propane heaters. It can cause dizziness, unconsciousness and, in rare cases, death.
Many propane heating units come equipped with an oxygen depletion system that shuts the unit off if the carbon monoxide levels rise to dangerous levels. Place the heater away from flammable materials, and avoid using the unit in small, indoor spaces. Keep a close eye on older models to ensure that the integrity of the unit remains constant to avoid fuel and gas leaks.