The dusty white coating on baby carrots is sometimes known as white blush or scuzz. Although it can be mistaken for mold or chemical residue, it isn't harmful.
It's common for baby carrots to dry out, and the white blush indicates dehydration. Contrary to what some people assume, the coating is not chlorine residue.
Sometimes, carrots that have had some abrasion will develop white markings from lignin, a polymer that the vegetable produces when they undergo stress.
Baby carrots are shaved down to remove their outer layer. The delicate inside flesh is now exposed to outside air, making them more prone to dehydration.
Producers of baby carrots will often try to combat this by packaging them with a small amount of water. If there is still white blush, soak them in cool water to remove the stains.