Why is my dishwasher stained brown?

Brown or black stains found in the dishwasher are usually from high levels of manganese.

Manganese that is dissolved in water can stain when the level is above .05mg/l. The dishwasher is a perfect mechanism to oxidize it because it heats it, agitates it and mixes the water with air. Manganese can also stain clothes in the washing machine, due to the same reasons. If bleach is added, staining is worse.