How to repair drywall that has adhesive patches all over from removing decorative mirror tiles?

Our 1970s original had these "decorative" mirror tiles on one wall when we purchased it. Of course we promptly removed them, but it left the drywall with patches of adhesive all over. How should I repair this wall - make it smooth again? I thought perhaps sanding all of the adhesive down, then applying new texture with a skim coat. But I'm definitely no pro at this stuff, so....suggestions?