You can buy gells that you paint on the wallpaper to soften the glue, and then you can remove it. That's what my wife and I did in the bathroom we remodelled. I believe we used "3M Safest Stripper". The work was a bit tedious, but the results have been good. We too had peeling wallpaper edges. I would not try to paint over that sort of thing.

Jonathan Gennick
http://gennick.com