The previous owner of my house painted before moving out. Instead of repairing nail and screw holes in the interior walls in the usual manner, it looks like he pounded them semi-flush, put on a little spackle, and painted directly over them. This has left dozens of raised bumps along the walls that are very visible and very ugly.

I know how to fix nail holes, but have no idea what to do about holes that have been ruined like this. Should I try to dig them out? Or would it be better to push the screws and nails deeper into the drywall and patch a slightly larger hole?

Is this even fixable by me or should I crack and hire somebody?