Wallpaper Didn't Stick?

We wanted to re-paper a bathroom. We took down the old paper, though it did not all come down, the vinyl layer came down fine, but the paper part stayed there. We used dry-wall mud, as we had also done a wall patch, for part of the wall we wanted to paper, due to a plumbing issue. We mudded the 'seams' between the previous paper strips, and in the area of the new drywall. There weren't many 'seams', but there were a few and then primed over the entire wall. The new paper seemed to go up fine, but two days laster it looks like it only stuck well in the parts where there was no old 'paper' under. The parts where the old paper was under there, even though it was mudded (in places) and primed over, the paper is coming off. I would have thought the primer would have taken care of any 'issues' in different surfaces. But the real question is, what do we do now? Can we take it down, and then put it back up with paste, or do we have to take it all down, buy new, and start over? Do we need to go back and take all that old paper off the wall, first? How? Another note, is that the paper we were using was over two years old, and had gotten a tad wet on one end, at some point (probably during the 'plumbing issue' that had caused the need for the patch to the hole in the wall). It had gotten wet enough to make it 'challenging' to unroll it, enough to make it stick to it's-self, though not too bad, while we unrolled it. It only tore all the way through all the layers in one small area, most of it was just the paper pulling off the back of the vinyl, in small sections on one end of the roll only. Is it possible that the glue is just too old? Or the moisture that caused that problem, must have made the rest of it less 'effective'? Though it did stick on the 'new' parts of the wall, just fine!