Kat,
To reiterate what I said on your other post and add to it, here's a few more comments. But no mater what I say or do, I'd suggest listening to Skip if he says different.
White vinegar kills and cleans off mold. So does bleach. Don't float the wood in it, just wipe it down good and let it dry. Also if you let the wood dry and air out from where ever it was, it will eventually loose the moldy smell.
If the old veneer is almost completely detached you can gently work it off with a thin blade, I use a hacksaw blade. Go in from every angle and pry up gently as you push the blade in. That way you can get most if not all of the old veneer off. Less sanding and surface prep if you can get the old stuff off completely.
I am no expurt by any means, but from the little I see there, I'd use the hacksaw blade or credit card to get the glue under the layers of veneer and then clamp and or weight it down. Then when all the loose pieces are glued, use an exacto blade and carefully square up the area where the piece is missing and graft in a patch. Keep the grain the same direction, then stain the patch to match the original parts. After that perhaps a coat of shellac and then some wax.
I have done that a bunch lately and if done carefully it doesn't look that bad and sometimes just disappears.
Joe