We use a square plastic container to put the washed dishes and stuff in while drying. We just bought a clear plastic storage box that fit under the sink and is big enough to hold a post dinners used stuff. When we do the dishes we take it out and put the washed dishes in the plastic box on the counter. If you're at sea you can put it somewhere snug while it's drying. (it also keeps the galley free from all those dishes)

Works great.

The other thing we started doing is to only have 4 of everything except for knives/forks/spoons (6 of each). Since it's only 2 of us on board there's no need for a service for more. If we have guests we use plastic disposable stuff.