First coat went on okay on kitchen wall where we took off wallpaper, but second coat is coming off in spots. What happened?
Probably didn't prime properly… I'll refer you to my page on wallpaper here: <a rel="nofollow" href="http://davmagic.com/paint/PAGES23.html" target="_blank">davmagic.com/paint/PAGES23.html</a>
There was wallpaper glue residue on the wall and the paint reacted with it is the most likely cause. Using a primer, an oil base primer like Kilz or shellac primer, would have prevented this. Actually using any primer would have helped, don't trust the paint to do all of the work even if it says paint + primer. Another possibility is applying the second coat too soon, the first coat wasn't dry enough.