Your dishwasher is supposed to clean your dishes, so it's a bit unsettling to open up a load of "clean" dishes and find a leftover brown residue in your appliance. The good news is that the brown residue is not necessarily a sign of trouble with your dishwasher; there are several possible reasons your dishwasher is leaving behind a brown residue.
What Goes in ... May Not Always Go Out
It's a dishwasher, not a garbage disposal. While most new, highly functional dishwashers do not require that you wash your plates before putting them in for the wash, there is such a thing as too much leftover food on your plates. If you put dishes with caked-on food into your dishwasher, there is a chance the dishwasher may be unable to fully wash away and drain these particles, leaving you with a residue made up largely of washed food. Try scraping off leftover food and rinsing your dishes before putting them in the dishwasher. If the residue disappears, you will know what was causing it.
Greasy dishes may not be filthy, but they can leave behind a residue in your dishwasher because grease is generally not water-soluble. If the dishwasher is not getting hot enough to dissolve the grease or your dish detergent simply is not up to the task, you may wind up looking at a greasy brown residue in the dishwasher after the water has drained away. It is not uncommon for energy saving tips to include turning down your hot water heater, but not having hot enough water can negatively affect your dishwasher's ability to clean your dishes thoroughly.
If you have hard water with a significant amount of mineral deposits, the brown residue you see is probably the result of mineral build-up. Calcium build-up is caused by hard water and can cause dark residue and stains if it is not regularly cleaned away with some form of acidic cleaning product.
Mold has a tendency to grow in wet places -- and dishwashers have a tendency to be wet a significant amount of the time. If mold manages to grow in your dishwasher due to too much moisture, it may have the appearance of a brown residue.