joint compound, oil based primer is a MUST

The Ben Moore paint site recommends using clear caulk to seal edges.

Here is a link that might be useful: Ben Moore - painting over wallpaper

Thanks to both of you for the tips. I'm embarrassed that I didn't think to look on a paint site for info.

My husband has suggested using a shellac based primer instead of oil based. It smells a little better, and dries faster. Any comments?

Don't try to stick it down. Remove it. Use a straight edge and level to mark and cut away the loose edge. Fill and feather the edge with drywall compound and sand it smooth.

Be sure to caulk the seams at the baseboard and any other wood trim. This will prevent future seam lifting. Caulk after primer.

Wash the walls before proceeding. Dirt will keep ANY paint or primer from adhering.

If the wallcovering is paper, you can use GARDZ as the primer, followed by two full coats of paint. If you need to block out the wallcovering design, your only choice is an alkyd primer, similar to Coverstain.

Brushworks, I don't understand your last statement. All I really remember about the wallpaper is that it is dark with ugly flowers. What should I be looking at?

coverstain would be best
your'e husband said shellac based would not smell as bad
he is very wrong
coverstain makes a low odor, which just means it does not small as bad as the regular
it still smells, but Bin smells way worse

If you need to block out the wallcovering design, your only choice is an alkyd primer, similar to Coverstain.

All I really remember about the wallpaper is that it is dark with ugly flowers. What should I be looking at?

Coverstain.

I think, maybe, you want, Coverstain

Well, after all that, she's decided to hold off for a while. But I'll mark this thread if/when they decide, or until it comes up again.

And Coverstain it is. :)