In two of my bedrooms, a previous owner put drywall up over the horsehair plaster, applied a layer of a fairly soft and chalky joint compound, and then applied a single coat of paint with no primer. The paint is chipping. In one room there are blocks about 2"x3" and in the other room there is a ring around every spot where a nail or screw has been driven into the wall. When we bough the house there were a few posters left up and when we pulled them off the tape brought up the paint.

I want to paint the rooms and am assuming that if I just paint over what is there it will accelerate the rate of failure. Is this correct? Is there an efficient way to strip the paint that is there? Is there a chance that the problem is the top coat of joint compound (again, it's fairly soft and chalky) and that even if I strip and paint, the new paint will simply chip off?

Any and all advice is greatly appreciated.