Hi,
First off, it's natural for the white coat of plaster to have spiderweb cracks all over the surface. These are only in the white coat and are very closely spaced and interconnected. By closely I mean 1/4" apart. _Those_ are nothing to fix or worry about. Cracks that extend into the base coat, and have movement that you can see by pressing, and seem "broken" are something to fix. I like to spray the cracks with bonding agent (garden sprayer) and sponge the stuff in (don't leave any drips of bonding agent; hard to skim over them). It seems to stop any movement for some time. Then add fiberglass mesh tape and the durabond routine, as you have read.
The closet area, maybe sand the mess a little smoother to take off any high spots, the prime and then tape. We always use an oil primer around unknown/unforeseeable problem areas, because it really seals anything "bad" like wallpaper glue and prevents problems in the future, and durabond or regular mud sticks to the primer. Regular mud is not optimal for plaster repair in areas where is has to build up thickness; that's where you run into drying cracks (plus it takes lots of time for all the water to evaporate) and when/if it ever gets wet again it falls off lime plaster in sheets. It won't fall off if you oil prime first, and use it sparingly. Use brown coat plaster like Structolite (or Gypsolite), on top of a bonding agent like Link or Plasterweld if down to the lath, use durabond or easysand when the white coat is damaged or missing, use regular mud only for small imperfections and the final touchups, and you'll be fine.
Casey

If the cracks are tightly closed,even on each side (no real height difference across the crack), and the finish coat is solid a coat of primer and two coats of paint should cover everything.

You do need to clean off all the old wallpaper glue.

Hot water and TSP make short work of it.

Wipe with an almost dripping sponge, let the solution sit on the wall a few minutes, then wipe off.
After it dries you should rinse with clear water one more time.

Allow to dry and prime.

Thank you both. I think I'll try washing the walls with TSP and priming. Do you have a favorite primer that you'd recommend for this job?

I do have a few small spots to patch, around new outlets and heat registers and in the corners of the room. The contractor has already started using premixed drywall compound on those spots. I know that's not desirable, but since it's already started, should I finish with that and just feather it into the existing plaster finish as much as possible?

etain, as to your last question; I'd say "yes". We've used premixed drywall compound on similar spots in our house and have never had a subsequent problem with them (some have been repaired this way nearly 20 years). The feathering into existing plaster finish takes patience and practice, but you can make it work. If the spots are small, you can blend the edges in with a damp sponge instead of sanding too.

The pink stuff didn't come off, no matter how hard I scrubbed with TSP, it must not be glue. So, I think I'm back to skim coating.

The walls do already have a number of pre-mixed drywall mud repairs that appear to have adhered well (even when a steamer was held over the spot for 30+ seconds multiple times). Would it be completely crazy to do a very thin skim coat with pre-mixed mud that I know sticks to the wall?

If I use Easy Sand, is it a good idea to cover the walls in a bonding agent or an oil based primer before applying the skim coat or would it be a waste of time?

We had pink plaster patches on some areas of our walls. Maybe that is what you have. I used Weldbond on the plaster that needed to be patched or skimcoated. Used a Magic Trowel (love it) to smooth out the new plaster and only used dry wall mud for small spots later on. I also used shellac-based primer rather than oil-based because in another room the paint peeled off the oil-based primer. Don't knnow why. We are very happy with the results.
Diane