It is permissible to disregard a tiny speck of black that can be easily brushed off of a bedikah cloth or that is identifiable as a foreign body. (A magnifying glass may prove helpful for this).
Other black spots may indeed invalidate the cloth, and should be evaluated by a halachic authority. When you have them evaluated, you can ask about how they are being assessed and how you might apply the principles used to checking your bedikah cloths in the future.
Please let us know if we can be of further assistance.