Painting on drywall that has been stripped of wallpaper?
I think you missed a really important step in the process. Anytime I have to remove paper from walls that were not treated with a release sizing before the paper was applied, the drywall paper is usually damaged or lots of glue residue is left behind. I have found that a skim coat of drywall compound needs be be applied, sanded and sealed with PVA primer before painting can be done.

In most cases, a self priming paint is only effective on previously painted walls, but never on new or bare sheetrock. The primer in those paints is designed for hiding old color, not sealing new sheetrock. New rock, skim coated rock, etc., need to be sealed with a quick drying sealer like PVA primer. This type of primer seals the porous surfaces and prevents the moisture in regular paints and primers to soak into the drywall.

The skim coat is actually the key step you missed. do not use untreated regular drywall compound for this job. Modify the mud with a bit of water and some Ivory dish liquid. A gallon of mud with an ounce or two of water and a couple of tablespoons of Ivory is a good formula. Mix well. It will be loose, almost runny. You will find it flows on very smooth without a lot of bubbles with a 8 to 12 knife or trowel. After it dries (8 to 12 hours), sand lightly with a 220 grit sanding sponge. Touch up any areas that still need attention, dry and sand. Clean off all dust with a slightly damp sponge, let dry then seal with PVA primer. You can usually paint in about 2 hours after PVA. 

As for the caulking you mentioned, remove as much as you can with a stiff one inch putty knife. Mineral spirits will usually remove remaining residue from the wood cabinets. Remove all of the caulking from the drywall with your knife, even if it takes some of the drywall paper with it. You can repair the divots in the rock with the skim coat as described above.