White patches on the concrete blocks are so-called fence "blooms". Mostly this is a cosmetic problem, these white spots poses no threat to the stability of the fence. Brick, stone, cement block, mortar, etc.  contain the water soluble salts, which causes white spots on manufactures. Atmospheric precipitation (rain, snow) also have these salts. The base of the fence is also likely to have the same salts. When the water reaches concrete, it dissolves the salts and bears them to the surface, after drying on the sun they appear as white spots. Salts which you can find in cement, curtain wall, the rock, finally one day dry out and the white patches disappear. However, this process can go on for decades. If every time you try to clean the stain with wet mop, you can make it worse, because of the concentration of dissolved salts, water absorbed back into the concrete, and after a while spots occurs again. If there is a lot of these salts, wire brush can be used. After that you need a soft brush to clean the salt dust. Acidic solutions and similar measures are only temporary assistance, because the pores of the concrete will absorb the salts again and after a while white patches will appear outside. The best salt stain remover is time. If possible, let the problem solve itself – the natural processes, over time, will remove the stains.