I think sometimes just the word "asbestos" much like the word "mold" automatically sends buyers into panic mode.
While both can be very dangerous an understanding of these and any real hazard posed (as opposed to a presence) is critical.
Asbestos was used in home construction mostly from around the 1940s up until about 1970. It was often present in attic insulation, vinyl tiles, linoleum, siding/roof shingles, paints, and window glaze/caulking. Unless your home is older, asbestos is likely never going to be an issue.
As for mold.... it is all about moisture and moisture control control.
Here are links to Environmental Protection Agency articles on both of these hazards.
Asbestos: In the words of the EPA "If you think there may be asbestos in your home, don’t panic." Follow this link to more information on asbestos in the home.
Mold: In the words of the EPA "Molds are usually not a problem indoors, unless mold spores land on a wet or damp spot and begin growing. Molds have the potential to cause health problems."
If you are in the market for a new home and either of these show up during an inspection it is critical to have the situation evaluated by a qualified licensed professional.