You said you sanded the spots on the wall are we talking drywall or plaster? Drywall isn’t as forgiving as a plaster wall. When one sands drywall they need to be careful not to break the paper surface or abrade the surface too deeply. The Nature of drywall is to be a somewhat durable but flexible product for wall covering. Unfortunately it does not have the smooth finish of a plastered wall and if your not a perfectionist and are easily satisfied with a semi- smooth finish drywall is a excellent offering for this purpose. Now paint drips are a bane to homeowners and unfortunately the persons who painted the walls prior to your purchasing the home weren’t concerned with the final outcome other than the placement of paint to hide paint that was dull, faded or otherwise undesirable. Now to the repair: Sanding the drips can be a tricky proposition you must not sand too deep or you will break the surface paper and repair becomes more like a plastering job and you will get surface flashing unless the area is primed, sanded, primed and then sanded again before being painted by back- tinted primer and matching paint. Sometimes it is easier to hire a professional who is familiar with drywall repairs, priming and finish painting of the walls