Before you start mudding:
Peel/scrape off the loose paper.
Prime the area with an oil-based primer and let it dry.
Peel/scrape off any remaining loose paper and re-prime those spots.
You may find a few bad spots after you apply the first skim coat. If
that happens, carefully remove the loose paper and give those spots a
quick shot of KILZ spray primer.
I've used BIN, KILZ, and a few other brands of primer for this
application and haven't noticed that one works better than another.
Zinsser makes a product specifically for this, but I haven't tried it yet:
http://www.zinsser.com/wtb-GARDZ.asp?SID=11&WID=27
Best method is to rip out all the sheetrock in the entire house and
start over. Why piss around with old junk....