The most effective method to fix your existing nail pops is to make sure that the head of the nail or screw is recessed about 1/32 inch. If it is sticking up, do not drive it too deep, or you will break through the paper surface. If you do, the drywall will be severely weakened.
Next, spread a little spackling compound over the nail pop area. Let it dry, and then sand it down. Lay a straight edge over it to make sure that it is not too high. A slightly raised spot is better than making it too shallow. Let it dry thoroughly, because the compound will shrink a little.
Paint the repaired area with drywall primer. Paint an area larger than the fixed spot so that the larger area will absorb the finished coat uniformly. This will make it almost impossible to detect that a repair was made to the wall.
Now back to your original question. The problem of nail pops can be caused by either improper drywall installation procedures by your builder or by damp lumber. Although lumber is supposedly kiln-dried, it can pick up moisture over time, especially if it has been out in the rain for a while.
Wall studs, which the drywall is nailed or screwed to, shrink as they dry. Unfortunately, they shrink the greatest amount (due to the orientation of the grain) in its depth dimension (nominal 4 inches).
If the drywall is nailed against damp wall studs and the studs shrink just a little as they dry, a tiny gap can form between the drywall and the stud. It doesn’t take much. If the drywall is bumped and pushed back against the stud, the nail head causes it to pop.
The best method to minimize nail pops is to use properly dried lumber. Since your project is a room addition, store the lumber in your garage, out of the rain, until it is used. If possible, delay your construction until the weather is reasonably warm, but not during high-humidity months.
Inspect the lumber as each piece is used, because alignment of the lumber is important to make sure that the drywall makes good contact with it. Your builder can use any bowed studs in other areas so that they are not wasted.
Make certain that proper drywall nails and screws are used and that they are of the proper length. These are different than ordinary fasteners. Drywall fasteners have specially shaped heads so that they do not tear the paper when they are recessed. For 1/2-inch drywall, 1-1/4-inch angular ring shank drywall nails work well.
If possible, have your builder wait a while to install the drywall after the wall framing is complete and the room is closed in. The longer you can wait, the better it is. This allows time for the framing lumber to dry and for the moisture content of all the pieces to stabilize.
The spacing of the screws and nails is equally important to minimize future nail pops and other problems. The maximum spacing for fasteners on drywall used for the ceiling is 12 inches on centers. This means that a four-foot-wide panel should have at least five fasteners. For wall panels, the fasteners can be 16 inches on centers.