PlantFiles is getting a new look! Just in time for spring, we're rolling out a new look for the best online plants database. It will also work with your smart phones and mobile devices, so now you can take it with you on garden center visits or botanical garden tours. Questions or comments? Please post them here.
They sell wood filler that you can use to fill in the dings, sand it smooth, and then stain over it and apply a coat of polyurethane in a finish that matches the rest of the vanity (matte vs shiny, etc). The trick will be finding a stain that matches the color of the rest of the vanity so that the patches won't be noticeable.
It depends on the wood. If it was real hardwood, perhaps a dampening then using a warm iron might bring the surface dent back up. If it is a vanier over particleboard - good luck - filling as already suggented and refinishing might be te best plan.