Water the grass and plants immediately adjacent to the moldy sidewalk. This may seem counterproductive, but saturating the ground creates a barrier so that your plants won't absorb any chemicals you use on the sidewalk.
Fill a bucket with water. Add 2 to 3 oz. of undiluted white vinegar to the bucket. White vinegar works well to kill mold and mildew and as a cleaner.
Power wash your sidewalk starting with the highest or farthest point from the sewer drain. Direct the nozzle toward the sidewalk so that the spray is strong enough to remove the discoloration of the moldy areas. Keep in mind that the spray is also degrading the surface of the sidewalk, so clean just enough to remove the mold and move on.
Activate the soap dispenser by placing the draw tube into the bucket with the vinegar water. Wash the sidewalk with the vinegar-enhanced water to clean and kill the mold as you wash the mold toward your sewer drain.
Wash the sidewalk all the way to the sewer drain so that no moldy water is sitting around where pets or children can walk through it.