I've dealt with wallpaper gunk and a few variables.
@87GN, Did the walls have a good paint coat under all that wallpaper? I'm also curious what type of adhesive was used. Answers to either of those two questions can affect the advice.
Scoring the paper generally means the walls should be sanded, patched, and sanded at the very least. Some of the peel and stick glues leave a lot of residue that make sanding near impossible. If there is good paint under the paper, it will help to soak and remove the residue before repairs. If the wallpaper was installed right over primer coat, things get tougher. I won't say impossible, but I've seen some that were close. The scored surface allows soaking to get into sheetrock paper. Adhesives bind to primer coats bind so well that it takes a lot of soaking to get the residue, bla, bla, bla. I think you get the point.
Some of those old school glues are pretty easy to remove. If that is the case, the residue may come off primer coat just by using a warm water solution. If you have old school glue on good finish paint, try using a wet sponge and a 4" joint blade to scrape. Those glues have less tendency to bleed through paint. A little residue won't be a deal breaker. You might get by with a good sanding.
A little residue can make a big mess. Often, it bleeds through or doesn't allow next layer to stick. If you're not sure, try patching or painting a test area and wait for it to dry.
It's a pain to do all those steps just so you can recoat. It's more of a pain if you have to do them over after you recoat.
One tool I've added for these projects is a basic drywall power sander. I have a lot of hours on my cheapo HF version. I must be around a hundred sheets on the thing and it's still going. Life is a lot simpler with that tool. It still amazes me that I waited so long to get one. I've done a lot of sanding and finishing over the years and tried all sorts of tricks. Those sanders make a big difference with messy big wall remodel projects. I do an initial sand and inspection before I even think about patching. Side lighting off the head also highlights any imperfections.