While acrylic products tend to be quite durable, they do require some special care. Like other plastics, acrylic surfaces scratch easily. Acrylic is lighter than glass, but because the material is softer it scratches easy. It's great that there are all kinds of common household fixtures now made with acrylic. And, the good news is that the scratches can be removed from them. But, with acrylic you have to be very careful to not make the scratches worse as you try to remove them.
Work with a clean surface. Use only products recommended for cleaning acrylic (see Resources below). Household cleaning products, like window cleaners, that contain ammonia are harsh and should not be used. Ammonia can make the acrylic look cloudy. Products not specially designed to clean acrylic can actually make small scratches on the surface. Do not use products that contain bleach or acetone either.
Blow off any dust or loose particles of dirt before you begin. Using a dry cloth will rub dust and dirt into the acrylic instead of removing it. Rubbing the dirt can make more scratches on the surface. Wet a soft cloth or sponge with a solution of warm water and a mild, liquid dish detergent to wipe the surface. Do not use paper towels either wet or dry, as they are well known for scratching acrylic surfaces.
Stay away from using abrasive cleaners and cleaning pads. Use a mild abrasive specifically designed for removing fine scratches from acrylic. Regular abrasive cleaners will dull the surface. Silver polish can be used as an alternative to polish out scratches if you do not have an acrylic cleaner on hand. However, test it on the surface first before using. Silver polish usually works well to remove light scratches from acrylic watch crystals.
Try using car wax to smooth out fine scratches. You want to use the rubbing compound type. Apply wax and buff out scratches that are deep enough that you can feel them with your fingernail. Buff in a round circular motion until the scratches disappear.
Sand deeper scratches with wet/dry sandpaper. Work with an extra fine grit paper such as 600 or 800 grade to smooth the surface. Saturate the paper in warm, soapy water before sanding. This helps keep the dust from scratching the acrylic more. Lightly sand the scratched area to a feathered edge. Finish by going over the surface again with an even finer grit sand paper like 1200 or 1500 grade.
Novus offers a selection of paste buffing compounds designed to remove both fine and heavy scratches, and abrasions from all kinds of acrylic and plastic surfaces.