Cut a bevel around the edge of the hole into the door with a utility knife.
Stuff the hole with crumpled paper or newspaper. This paper will provide the base support for the material that will fill the hole, as described in the next step. If the door is solid, fill the hole only if it is deep.
Insert the tip of an aerosol foam insulation applicator into the hole. Depress the tab on the can to fill the door hole with the material. Allow the insulation to dry.
Trim off the excess insulation, once dried, with a sharp knife.
Mix polyester resin with its included catalyst according to the manufacturer's instructions. Then smooth it over the door hole with a plastic putty knife.
Trim off the excess resin after it begins to get "rubbery" with a sharp knife. Cut away the excess to create as smooth a surface as possible.
Sand the surface of the hole with a 100-grit sandpaper.
Smooth joint compound over the hole with a plastic scraper. Then use a wide putty knife to smooth and remove the excess compound before it dries.
Sand the surface of the joint compound with a 100-grit sandpaper.
Paint over the dried joint compound with a brush to blend it with the door.