Screws for drywall ceilings should be spaced every 1 foot apart in a grid manner in both directions....side to side and end to end and around the perimeter as well. The head of each screw must not break the paper facing material of the drywall.. just set slightly below the surface or creates a dimple such that the head of the screw cannot be felt on the surface which allows for drywall mud to cover them. Use a drywall screwgun or a tool called a "dimpler bit"...sold at home centers and hardware stores... that attaches to a standard drill or drill extension bit to set the screws properly if you have problems with gauging how deep to set screws properly. If you set screws too deep, then the screws have less holding power and will or can rip right through once the drywall is allowed to hang on it's own....especially if they are set too far apart or not enough screws per panel.

Replace the damaged drywall with a new panel or reinstall the sheet back in place and rescrew in new areas... keeping 1 foot apart and at least 1 inch away from old holes....use drywall compound to fill old holes . Drywall for vertical walls can be screwed every 16" in a grid pattern and along edges.

On sheets of 1/2" drywall,(or 5/8" for that matter) you may notice that the long edges are slightly tapered and less thick than 1/2"....they have a tapered edge which is only 3/8" at the edge thick to allow for coats of drywall mud to cover the joints with a smooth surface so it allows for an 1/8" of mud at the very edge and less so as you go a few inches inward. The edges can be somewhat harder to set the drywall screws so if the screw heads in those areas are flush or stick up less than 1/16", they will still be covered with mud and hold just as well as dimpling. I often go back after a sheet is installed with an impact or cordless drill and a #2 hardened bit and set the heads of screws along the edge slightly below the paper surface if they are hard to set with a dimpler.

Make sure the wood furring strips are attached firmly to ceiling joists....any screws or nails should extend at least 1" into the joists....I.E....if the wood strips are 3/4" thick, use 1 3/4"- 2" nails or screws to attach them to joists and predrill pilot holes for nails or screws in the strips so wood does not split if that is a problem on the ends.