Robert: Our privacy fence gets exactly what yours has on the cross support rails. It's probably mold. (If it comes off with a scrub brush and some dishwashing detergent, it's definately mold. Cleaning this way would not alter a bad stain job)Yes, power washing will remove it, just don't get too close, it will blast the wood to pieces and remove the stain. (learned that one the hard way). Or, you could just clean all of it with the scrub brush (a deck brush with long handle makes it easier). You could put a bit of bleach in the water, if you put an inexpensive tarp or something down to protect the grass. Mold comes off pretty easily, and once you get it off and the wood has dried thoroughly, put a coat of Thompson's Water Seal or similar product on to repel moisture. You will find that it tends to return (primarily in spots hit by a sprinkler, or in more shade than sun). We have to put our sealer on about every 2 to 3 years. You can also purchase stains that have water sealer in them, if you choose to go that route.