My two cents:
A RV furnace is pretty safe. One vent is an intake for air for the combustion process. The other is the exhaust. The air is heated, then blown through a heat exchanger. Inside air is sucked in through the exchanger and heater. The two pipes of air never cross, unless one has a cracked exchanger, or one has a window open right by the exhaust vent.
The next on the list are electric heaters. It might be safe enough to run the full 1500 watts that a heater on high uses. I don't trust RV wiring in all but the higher-tier rigs, so I will run it at 750 watts. I then use a heavy-duty extension cord (10/3) and thread that through the mousehole for a second heater. Some Vornado heaters are US made, others from China. In the past, I've found them extremely safe/reliable.
As for propane heaters like Buddy heaters, I had great luck with one in a tent where I had a good amount of air exchange up and out the rainfly. In a closed RV, it might be safe, but there is the danger of CO/CO2 which was pointed out. Last year, someone where I was camping had their RV burn down because bedding or something caught. This isn't the fault of the heater, but I prefer not to use one unless I have no other options (RV furnace not working, generator inoperable, etc.) Of course, there is the fact that the propane heaters put a lot of water in the air which can be a problem.
If I had to use a propane heater as a last resort, I'd probably put it on a baking tray on the stove (so it is on an even surface), open a living room vent, open the bathroom vent a tad, and use 1-2 O2Cool fans to keep the circulating. That way, all the hot air doesn't just float to the top and out the vent.