I assume that there was a paint or some type of primer under the wallpaper? You need to be sure that all the adhesive is washed off.

Wallpaper adhesives will react with latex paints and cause problems in the humid enviroment of a bathroom.

Wash the walls with clean water several times. If you can feel a "slimeyness" to the walls, then you still have paste on the wall. Afterwards, allow the walls to dry for a day. Then your ready to do any patch work, prime or spot prime, then paint as you normally would any room.

I agree you need to get all the paste residue off or it will cause you problems.

I would plan on priming the entire wall surface, and you should use an acrylic undercoater to prime with as they have the best adhesion and moisture resitance. Your local paint store can help you with getting the correct primer. The finish paint should be an acrylic eggshell finish if the bathroom is used for showers and baths and plan on putting two coats over the primer.