Drywall hole, plaster, Primer and Paint

My guess would be that you didn't prime and that you tried to paint over oil paint with a latex paint or some incompatible combination of paints like that.

You should figure out what type of paint was used for the original coat and purchase a suitable primer to go on top, and then apply your new color. If you really aren't sure, someone at a paint store can recommend a primer that is suitable for a range of scenarios.

Based on the picture I would probably avoid a paint-primer combination product.

Primer is typically pretty cheap so aside from the additional labor and time, it should not add considerable costs to your project.

There are a few reasons that paint wrinkles. The most common reason is using an oil based primer or paint over a latex painted surface. If you only have a small area of problem, this is probably not the case. I suspect you may have left some wallpaper sizing or glue behind. Some soap may have leached behind the wallpaper also. When removing wallpaper, it is very important to really clean the surface well. Sometimes a skim coat of joint compound is needed to smooth the walls and create a good bondable surface. Another possible cause is that the primer was not dry enough when you painted. If the primer didn't wrinkle after it had been on and cured, then maybe something contaminated the surface before you painted. As you see, there are several reasons for the paint failure. Check the options or add more detail to the question.