It is actually pretty high on the list of reasons why people crash airplanes. You get carbon monoxide limiting your blood's ability to absorb oxygen and then you fly to altitude in an unpressurized aircraft. It is a recipe for disaster. Just about every large aircraft supply business, flying advocacy group, and flying magazines, etc... practically give away the cheap dead stop style carbon monoxide detectors.
I didn't realize the cabin heaters on small planes are like the VW heater — a counterflow gas/gas heat exchanger no doubt prone to corrosion and leakage.
On a small aircraft they are typically just a sheet aluminum shroud that covers the muffler with an air inlet that gets fresh air from the nose of the aircraft and one outlet that goes to your cabin heat and another that goes to your defroster. You control these with valves have cables that go to levers or push/pull knobs on your control panel. ...
The VW system is likely less prone to failure. But the muffler on an aircraft is supposed to be carefully inspected at each annual inspection and often at designated time intervals. The Piper Cherokee we purchased had just received its annual inspection the week before. When I contacted the mechanic, he was very willing to assist me for no charge.