No, patio heaters are not dangerous… Unless, as is the case with all gas and electric appliances, the safety instructions that come with the equipment are not followed. Ensure that the heaters are not misused, or setup/used incorrectly.
Gas Patio heaters are designed for outdoor use only and do emit some fumes that you wouldn’t want indoors. Also the hose and connections between the gas bottle, regulator and the heater do need to be checked regularly, making sure that the connections are secure and that there are no leaks.
Electric patio heaters don’t give of any fumes or dangerous radiation. The heat is transmitted in the form of safe infrared light. Other than an occasional clean, they don’t require any maintenance so all you have to keep in mind is the fact that a heater is HOT - Please ensure that you follow instructions related to safe clearance around the heater.
In short – patio heaters are safe if you follow the instructions provided in the manuals.