What do I do with all these Special ?

I've done a hand full of Urgent Quests and such and I'm DROWNING in unidentified weapons that I can't use. Is it even worth identifying them? Should I junk them at the shop or is there something else I can do with them?

If you are doing the UQs on a high enough level, there is a good chance that many of those could be 10☆ and 11☆ weapons that you can then turn into ExCubes and/or Photon Spheres. Plus, if any among them happen to be 13☆s, you wouldn't know until you go to appraise them since the rainbow 13☆ icon only shows up when you go to appraise, and not in your Inventory.

Well, they were all 8☆-9☆, but I guess it's better knowing than not. Is there any indication that I should look out for to use the enhanced appraisal?

@Reaped-Psyche You could consider using enhanced appraisal if it is a 13☆ (rainbow icon at appraisal instead of just grey), though typically under the conditions that you can personally use it or sell it on the Personal Shops (assuming that a 13☆ of that weapon type, regardless of the specific weapon itself, is worth more than the enhanced appraisal cost).

Awesome info. Thanks!