there are different possibilites: Blackwater might be treated onboard so that under certain circumstances clearly defined by international laws, it might be released into the ocean, or it will have to be taken off the ship in port.
Dumping untreated blackwater is not allowed however. Even though, as you write, it does happen from time to time - either on purpose or accidentally.
Relatives of ours live on the beach at Cape Cod. For lack of a better term, women's products, and a lot of them, are washing up on shore. They, along with other residents, have to go down to the beach every morning with bags and clean up.
Environmental Conservation has become involved because it's gotten so out of hand.
My point is... if dumping of "plastic applicators" are washing up, what's a little black water?