Sand the area surrounding the door using a sanding buffer with a medium-grain sanding ring. This will make the wall around the door more even and remove any large areas of roughness. Focus on the cracked section.
Sand the same area using the sanding buffer with a fine-grain sanding ring. This will make the wall around the door smooth and even.
Tear off a piece of plaster gauze, dampen it with water, then spread the plaster gauze over the cracked areas. Keep the gauze as taut as you can and smooth out any folds or bubbles. Allow the gauze to dry for 2 hours.
Spread a goodly amount of spackle on a trowel, then scrape the trowel over the wall where you applied the plaster gauze. This will blend the spackle over the gauze and wall to make the area appear flush and congruent. Repeat until the cracked sections are completely concealed and even. Allow the spackle to dry for 4 hours.
Sand the area you speckled with fine-grain sandpaper, moving the sandpaper in small, circular motions. This will further blend the spackle flush with the wall. Wipe off the area with a dry washcloth.
Fill a paint tray with latex paint. Apply the paint around the door frame using a 2-inch flat paintbrush.
Apply the latex paint to the rest of the wall using a paint roller. Allow the wall to dry for 12 hours.