Oh wallpaper, how I loathe thee.
First, you're hideous
Then, you firmly stick to the wall, coming off only in minute pieces of confetti
Next you must be scrubbed to remove traces of glue
And finally, your glue is never really gone, so you must be covered in oil-based primer
I talked to a handful of experts, and it turns out that even though I scrubbed the heck out of the walls to get all the wallpaper glue off, it's still a good idea to prime before you paint.
Wallpaper glue can become reactivated by water-based paints like the usual latex you'd use on walls, and cause bubbling and peeling and all sorts of mess I don't want to deal with.
Priming the walls with an oil-based primer seals in the glue and saves the day. But nobody warns you that it smells horrible.
I bought the "odorless" oil-based primer Sherwin Williams offers, and went to town. Coverage was OK, I suppose, but the smell was AWFUL!!! Odorless, my foot! We aired out the room for days and it still lingers. Bleh. Hopefully the normal latex wall paint will seal in the odor?
Anyways, now it's done and ready for pretty, zero-VOC paint. Thankfully it'll be a while before we're hosting guests in here, so it'll have plenty of time to air out.