Check the horizontal pipe between the disposal and drain on right. If it is not downhill enough, water will sit instead of run. I've seen all kinds of black gunk accumulate because they weren't piped with any slope at all. Usually the cheapest double bowl drain kits don't have adjustment. I've dealt with this on my own kitchen and one other.
Start by just eyeing it and see if it actually slopes toward the drain side. If not it's not right.