There can be reasons for unstable walls, mostly cheap or poor quality paint, dust, someone applied paint over dust, improper prep, incompatible layers inside the wall built up over years (oil based paint, latex paint, dust, gloss paint, joint compound, etc.).
These can cause problems with wallpaper, mostly with the layers delaminating (coming apart), which causes the wallpaper seams to come away from the wall. Sometimes sheets of wallpaper simply fall off the wall.
This isn’t so much a problem with paint, because it just sits on the surface. But wallpaper shrinks when the paste dries, or expands and contracts with humidity, and can put tension on the seams
Before wallpaper goes up, one way to test for such unstable surfaces is the tape test . Use a razor blade to cut an “X” into the wall, scoring through the paint and maybe into a few layers beneath. Place a strip of blue painters tape over the cut. Pull the tape off the wall.
If paint comes away from the wall along with the tape, or if layers inside the wall come apart, you know you have to do a lot of specialized prep to stabilize the wall before hanging / installing the wallpaper.
This example is an interesting twist. The homeowner used a piece of tape to hold up a wallpaper sample. Then used an ink pen to write notes on it. When removed, the tape took the paint off – in the shape of the writing!
The Wallpaper Lady's Blog 