The link to the Antique Auto Club thread is useful, particularly the info posted by Mark DeFloria.
As a EPA and STate of Hawaii licensed Asbestos Project Designer, I've written asbestos abatement specifications for 15 years. The key points are to identify the material, and if removed, wet it thoroughly, remove it intact to the extent possible, have a fan or breeze blowing any possible dust away from you, and use a NIOSH-approved (not OSHA, they don't approve respirators as one poster suggested) respirator, with HEPA-rated filter cartridges.
2x on Murray's survival, particularly in light of his smoking, which has a nasty synergistic effect in combination with asbestos.
Latency periods for asbestos-related diseases (asbestosis, lung cancer, mesothelioma) range from 10 to 30-plus years. Odd thing is that although the first two have a well-defined dose-response relationship, you can get mesothelioma from only a single exposure, 40 years later. Murray may get it yet!
We get calls from persons who ought to know better than to disturb products like popcorn ceilings, usually after they've made a real mess. I tell them to take a little bit and crush it between their fingers, then snort it through a straw just like cocaine, and call me in 20 years if they're sick. NOT! Then I suggest the poor man's assessment: hold a little bit in a pair of tweezers and put a lighter flame to it. If the fibers curl and burn, not likely asbestos. If the fibers sit there and glow, you may have a problem. Testing by Polarized Light Microscopy is about 20 bucks per specimen.
Asbestos was used for thermal insulation, electrical insulation, and as a thickener to products that otherwise flowed too easily. There were thousands of products which used it; most are gone. The friable form (can be crushed to powder by hand pressure) is most dangerous because it most easily becomes airborne fibers. Nonfriable forms (9"x9" floor tile is very frequently asbestos-containing) are less likely to produce respirable asbestos.