Besides Mesothelioma and asbestosis, asbestos exposure can cause serious blemishes called asbestos warts, which result when the fibers get under the skin. As ugly as they are, it's probably not worth trying to litigate a case for this illness; the courts are too full cases regarding the more serious aspects of asbestos poisoning.
It's hard to determine how much asbestos exposure is too much, but a good rule of thumb is that all it takes is a few weeks or months to inhale enough to cause Mesothelioma somewhere down the road. The longer you were exposed, the better your chances of winning an asbestos claim in court.