Update 10/30/2012: See comment I left under gregmac's answer
I just finished installing QuietRock 525 over existing walls. Half a sheet of 525 is heavy backer board and I am thinking that's the reason why several of my screws are having so much trouble recessing into the wall. If I had known in the beginning what I know now, I would have installed the QuietRock as the first layer and used special backer board screws with a square-shaped bit since this phillips bit wants to slip out of the screw head with a loud "ratta tat tat!".
So now I am stuck with some screws that stick out slightly from the surface of the drywall. It's not as much as 1/16" or anything, but you can feel it raise as you take your finger over the head. I could remove the offending screws, drill out a wider hole, and screw them back in, but I don't want to deteriorate the integrity of the grab.
I'd like to finish over them so that the wall is smooth. What do I do, tape over them? Use an extra-thick layer of mud? Eh?
Best Answer
Though you might be able to mud over them, you're looking at 1-2' of mud (feathered) around each screw to make it not noticeable, which basically means you'd be covering the entire piece of drywall with mud. Like pretty much everything in construction, it will be much easier to do it properly now rather than try to fix it later.
If your driver is slipping out, you are probably not using the right bits (or your bit is worn out) or are not pushing hard enough on the drill to prevent the bit from slipping out. Make sure the bit fits well in the screw head: it should not have any room to wiggle in any direction, and should not slide around. #2 Philips is the usual here, but depending on the screw head it may need to be a sharper/longer or blunt tip.
It could also be that your screws are not the right type. If you're going into wood studs, generally you should use coarse thread screws. If you're going into metal studs, it should be fine-threaded screws.
Since the board is also 5/8, it may be that the screws are not long enough. Try longer screws, which should get a better grip on the studs behind so once they start going in, they'll go in as deep as you need.