What is the white “dust” mold that develops on mulch? Does it present a danger to my plants, pets, or family members?

This is actually the remains of a Slime Mold. Slime Molds are easily identified by their pink, yellow, or orange colors. As they dry up, they leave a white powdery residue. This is actually part of the natural decomposition process and though it can be unsightly, it is not harmful. You can usually fluff the mulch or just remove it altogether if you would like. Note: decomposed mulch can help with water retention of your soils.