Do you have a bathroom over the bedroom or is just the roof over it? You might have a slow leak that is causing it to sag. You can check this by using a moisture detector and sticking a small pin-like device into the drywall to detect moisture content. If it reads above acceptable levels, you'll likely need to open up your ceiling to determine the source of the leak - and then fix it.

If there is no possible way that you have a leak or if you did the test above and nothing was out of the ordinary, it may just be due to time and gravity. Even houses sag as they get older - just like us! Most drywall used to be hung with hammer and nail, these days people are using drywall screws which will continuously hold the drywall tight to the studs or joists (depending on where it's hung). So if you have nail pops, the best bet is to pull the nails that have popped out with the claw of a hammer and then in a slightly different location, reattach the drywall to the studs (or joists)to suck it tight. You might consider building a temporary brace out of 2x4's while you do this to support the drywall. If it's been sagging for a long time, the entire material may be warped and may require replacing, but try this method first.

Once you have reattached the drywall and it's now tight to the supports, simply fill in the holes with spackle, sand smooth and paint.

Good luck!

Normally, "nail pops" refer to nails that don't hold the drywall tight against the framing memeber (usually because of warped studs), leaving some play between the wall board and the studs. Then, when something is pushed against the wall, the wallboard goes flush to the stud, and the nail head ends up "popping" through the surface of the drywall finish, leaving a slight bump. Nail pops wouldn't make sense on a ceiling, and especially not a sagging one. I'm guessing you have nails that have pulled through the drywall (blow-outs), leaving holes where they've pulled through the drywall?

If you don't have water damage, and there's nothing sitting on top of the drywall (I don't suppose there's an attic/crawl space above the room with boxes stored in it? any chance something's sitting directly on the drywall?), the failure was probably caused by the original installer overdriving the fasteners. The strength of drywall is in the paper facing, and a properly installed nail/screw just dimples the surface. If you overdrive the fastener, it will eventually pull through.

User drywall screws, not wood screws. Drywall screws have a different flare than wood screws. With older lumber, you'll probably find the fine thread screws drive more easily, but either coarse or fine thread will work. To make sure YOU don't overdrive your fasteners, pick up a drywall-dimpling bit. It's basically a screwdriver bit with a collar that causes the bit to disengage the screw head when it's just the right depth below the wall surface. You'll find them in the drill bit section at your local home store, but it may take some searching as they're not a big seller. DeWalt has a 3 pack for about $3.00 in a small (2x3) plastic bag.