Clay is Plainsman M370. This is part of the aging process and can appear on any clay, depending on the conditions of storage (especially if stored in a very warm place or one exposed to sunlight). On the right this material has been fired to cone 6. The spots, although dark in the wet state, are burned away during firing. Mixing these specks back into the interior of the slug can be done quickly by wedging (diminishing worries about any allergy issues).
The process of mixing a plastic clay by hand before forming it. Similar to kneading of bread dough, it is considered an essential step by most potters.
Ceramic glazes and clay bodies can host micro organisms. They can be just a nuisance, a source of worry or they can render a product useless. What should you do?