How can I properly prep a wall for painting after stripping wallpaper?

I have stripped vinyl wallpaper off my entire master bedroom. The vinyl top of the paper came off easily. Then I wet the paper backing and gradually scd it off with a putty knife. There was a lot of glue left on the wall which I washed off with detergent and hot water. The problem now is that in some spots I am down to the clean paper facing of the drywall and in other spots there is a hard coating (which I presume is either a primer or sizing) left on the wall. If I paint the wall as it is, all the little raised edges between where the leftover coating is and the bare drywall will show through the paint. Is there an easier way to even out the walls without skim coating everything with joint compound and sanding. That is such a big task and such a mess. I don't think I can sand the edges because I will tear up the bare drywall. Does anyone have any other solutions?