i have had similar problems with the walls and ceilings in my house, which is 50 yrs old.they are all wallpapered and i am modernising each room as i go along, taking off the paper with a steamer.in the first room i went too quickly and whilst i removed the paper and its backing i did,nt always remove the adhesive which when left behind is a real pain.
not as thick as your paint but still enough to cause a blemish when i repaint, if i didnt go back over it.
this is not much help to you this time but i sent it for the future.try a steamer but be careful as it a fine line when judging between enough heat applied and too much cracking the skim.
also for wall repairs to small cracks and marks a product called easifill is brill, green/white bags b&q �10.50 in the plaster section. dont apply it like skim, keep it high and proud, not flat.its a doddle to rub down if a bit dusty