John, I saw these many times in the 20 years I spent as a professional home inspector. With the older 80% efficiency heating systems, they seemed to work fine but you need to keep in mind that higher efficiency systems that emit combustion gasses at a much lower temperature. Since the asbestos pipe is not insulated, you could develop backdraft (carbon monoxide) problems that would be unsafe.Since this is cement asbestos, fibers are contained in a binding agent so risk of exposure is minimal. The only hassle will be disposing of this after it is removed as it usually needs to go to a hazardous waste disposal facility, just like old paints, oil, etc. If you are going to replace part of this, my suggestion would be to just replace all of it at that time. I would not spend money attaching a new vent pipe to an old asbestos pipe. Check with a heating contractor to find out what vent pipe you need for your system but most use "Class B" which is a dual wall vent pipe that is sold in sections and just snaps together.