I recently removed the wallpaper in our dining room. In doing so, some patches of paint came off as I was scraping. Some just the top layer of paint others down to the drywall. What do I need to do to those areas if anything before I paint? Will they show through?

 

They will show through. What you do is up to your level of commitment. You can scrape/sand bad areas, apply spackle to them, sand smooth and paint away. You should be fine just using this method. Another way is after you repair these areas, is to coat the wall with a good quality sealer. This should seal through the patches, paint layers, and to the wall surface, firming up the entire top layer so this problem should never occur again. The latter is definately the preferred method, though more expensive and the fumes from some primers can cause Excedrin headache #32. Best of luck with your project.