Trim any loose leather from the scratched area of your couch with a pair of scissors. This prepares the surface for sanding.
Sand the area with a piece of 1200-grit sandpaper as long as the palm of your hand until you come to a smooth finish.
Clean the area with a cotton swab dampened with isopropyl alcohol. Allow 10 minutes to pass before continuing to work on your leather couch.
Spread a thin layer of heavy-leather filler with a palette knife wherever you see scratches and/or holes. Let five minutes pass before you sand the area again with 1200-grit sandpaper. You might not like how it looks right now, but you haven't applied any color yet.
Dip a small sponge into leather paint and skim it across the previously scratched area on the couch. Try to get the first coat as uniform as possible. Follow label instructions for waiting time between coats, allowing the first coat to air-dry before applying a second coat in the same manner. Allow the second coat to air-dry.
Spray a thin layer of lacquer evenly to the area on your couch you just painted. This gives it a glossy finish and protects the paint. With such a finish, no one would know there were cat scratches on your leather couch.