Moles and melanoma appear to be on a continuum under the microscope, from the most benign garden-variety moles to dysplastic nevi with mild atypia, moderate atypia, severe atypia and then melanoma.
The concept of dysplastic nevus is controversial. We know dysplastic nevi are a marker for higher risk of developing a melanoma, but we don't have any evidence showing that they themselves (the dysplastic nevi) are precancerous lesions.
There is no good scientific way of studying it prospectively, meaning there is no way to know something is a dysplastic mole without biopsying it, and biopsying it means you are changing the nature and behavior of the lesion, so what it will do in the future is not necessarily what it would have done had it not been disturbed by the biopsy. So we can only analyze things by looking back. And looking back, melanomas arise primarily on normal skin, and much less often in a mole. The statistics are about 20% of melanomas are seen in association with a mole under the microscope. So theoretically if one removes all the moles they have, they are decreasing their risk of melanoma by approximately 20%. Not great numbers.
So my approach is that I remove lesions that I find suspicious for melanoma, such as those with Asymmetry, Border irregularity, Color irregularity, Diameter greater than 1/4 inch (not the most reliable indicator) and any Evolving or changing moles. This is the so called ABCDE rule.
When I remove suspicious moles, it is because I am concerned they may be cancerous, and I excise them with sutures in an attempt to remove the entire lesion with a margin of 1-2 mm of normal tissue. Most of the time, that way the entire lesion is removed. However, I recommend re-excision of all moderately and severely atypical moles that were not completely removed by the initial procedure.
For people with a large number of atypical appearing moles, one of the best ways of follow-up, aside from regular total body skin examinations by a dermatologist, is total body imaging with a system such as Melanoscan, where the skin is imaged and photographs are taken so that they can be compared easily on subsequent visits. Early and subtle changes can be detected this way.
Not everyone needs such a sophisticated screening method, but people with a large number of large atypical moles, particularly if they also have a family history of melanoma, would benefit from such imaging.