Conophytums have few problems with microbes, if you treat them right. Plants can come down with fungal or bacterial rots; these diseases almost always indicate that the victims are not getting enough light, or have been grossly overwatered. Properly grown plants do, on very rare occasions, rot for no apparent reason; the only effective treatment once rot starts is to excise the affected parts. I have a feeling that plants in organic soils have more disease problems than those in mineral soils, but don't have the data to rigorously prove it.
Conos are generally pest-free as well. The only insect pests I have had problems with on adult plants are mealy bugs, in particular the dreaded root mealy bug. Mealy bugs are basically impossible to eradicate in a large collection, but you can keep them at bay. Wipe off small infestations with rubbing alcohol. For heavily infested plants, unpot the plant and wash off the bugs in soapy water. A good dose of orthene or some other systemic insecticide will apparently clean up a collection fairly well, although I haven't been desperate enough to try it myself (yet).
Seedlings may be attacked by fungus gnat larvae. Cultural remedies that reduce the growth of the algae and fungus that are the larvae's chief food source can be effective: provide good air circulation, and let the soil surface dry a bit between waterings. The number of adult gnats can be greatly reduced by a few yellow sticky traps, or by growing some sundews in your seed raising area.
One sometimes has troubles with vertebrate pests, such as mice, birds, and people. Probably the best (if not the most environmentally sound) way to deal with rodents is with poison bait. Birds, which seem to like eating mesemb seedlings, can be kept away with screening. Human pests disturbing or stealing plants are a threat in public greenhouses like the one I use. Extra vigilance, barriers, and carefully placed anti-personal mines are all excellent control options.