Hi! The old wardrobe won't load for me and there doesn't appear to be an option on the new wardrobe to change my HA's mouth. Am I missing something?

Bad news. It's a site bug. There's a topic that discusses/complains about it here

Say it ain't so! I'm able to change my eyes and skin, though? The tab loads, just no lips or nose options.

Skins, base colors, eyes, and hair seem to be working in Beta currently. Sadly we're just going to have to wait on wardrobe V3, for our mouths and noses. Per Keith, the original wardrobe is unfixable, and they never got around to getting the nose and mouth options on Beta before it became obvious that it wasn't going to work either.
Hopefully something will be in place by Masquerade at the very least. (fingers crossed)