Duke William of Normandy won the battle because was well prepared and had a good army. They prepared carefully for the battle. The Normans had knights on horseback who were skilful fighters.
A utility knife, metal ruler, and a hammer can be faster than trying to carefully saw an opening. Score the drywall a couple times till you are most of the way through, then just knock a hole with the hammer and break the drywall back at the score lines.
If it's a screw, drive it in a little tighter by hand. If it's a nail, use a nail set and a hammer to drive it about 1/8 inch deeper. Push on the wall to see if it flexes. The drywall could have separated from the studs. If so, you should drive in some 1-1/4 or 1-5/8 drywall screws, above and below the nail pop, to better secure the drywall. Then fill the holes with a setting type of drywall patching material.