Dirt, leaf tannins, rust and other minerals can stain the finish of your plastered pool. If the stain is organic; left from a leaf or acorn for example, a small amount of granular chlorine added at that location and allowed to settle on the stain will usually remove it instantly. Other non-organic stains will not be removed by chlorine. Do not place chlorine tablets directly into the pool...they will stain and etch the plaster.
If chlorine doesn't work, acid usually will. Draining and acid washing will remove a thin layer of plaster (and stains), exposing fresh, new looking plaster beneath. A No-Drain acid wash can also be performed, with varying results. For localized stains , a stain master tool can be used to deliver acid directly to the stain. Stains can also be sanded with pumice stones or wet/dry sandpaper.