I am removing wallpaper. After I am finish, I will use my magic trowel and skim coat the walls with thinned out joint compound, and then I will paint the walls. My question: how diligent do I have to be about removing paper? The wallpaper is not cooperating and bits and fragments spot the wall, and I don't want to spend the night removing every little spot if I do not have to. Can I just put a skim coat over the thin layer of paper that spot the wall? This is just the thin layer of backing that stays behind when the paper is removed.

This is a bathroom.

Thanks for any guidance.