Issue: Approve/Deny Link needs separation

To permanently delete edits, the moderator must have permission to permanently delete posts in the same forum. Also, the moderator must have permission to rollback edits. This is not a function of the ModCP. Like approval, this must be done from the article's history tab.

Where do I find these settings?

Permanently removing posts should be a permission under the user's Moderator Permissions, which you set when you edit that moderator.
As for rollbacks, make sure that the moderator usergroup has this wiki permission.

We are not talking about roll back or removing posts, but about purging moderated edits. Where can I set the permission to allow a moderator to do this?

There is no separate permission to purge moderated edits. As mentioned above you need both #1 AND #2:

#1 You need moderator permission to remove posts -- because removing the only visible revision can permanently delete the article.
#2 You also need permission to rollback -- because removing the current revision effectively rolls back the article, and because this permission is needed to handle any moderated revisions.

Another thing to keep in mind is that VaultWiki 3.0.14 removed incorrect messages to moderators about edits needing moderation. VaultWiki 3.0.11 - 3.0.13 said that the public versions of some articles needed moderation even though they had not been edited or had already been approved.

As in permission to permanently delete wikis, threads and posts?? (which means they can hypothetically delete the whole forum content) Or just to soft delete posts?

Where do I find this setting?

#1 Yes, permission to permanently delete content. When you purge the edit you are permanently deleting it, so you need this permission.

#2 The rollback permission is the same as the "undo edits" permission that is under VaultWiki Permissions for each usergroup.

I see. There is a big difference between allowing someone to purge new edits and to allow him to delete your entire forum. I really cant give that permission to anyone below administrator status. I had more than a few situations on the last decade where a moderator or someone who gained access to a moderator account would have deleted everything if they could have.
Please rethink this function and add functionality that will allow staff to deny a new edit, while not giving functionality to delete posts and threads.

I think you are somewhat confused about the difference between PURGING an edit and DENYING a moderated edit. A moderator can DENY or APPROVE an edit without purge permissions. To deny/approve, all they need is "undo" permissions.
After being denied, the edit will still exist, but it will not be visible to normal users, and it can't be reinstated after another edit is made.

PURGE refers to permanently deleting the edit (i.e. removing the content from the database). This is just as powerful as deleting threads and posts and in the hands of a malicious user can end with them deleting your entire wiki -- Let me try to explain again: if a moderator PURGES every edit of an article, okay sounds fine, but when they get to the last edit on the article, then the thread is also purged, because it no longer has any text. Additionally, any comments (posts) on that article are purged. This equates to the moderator deleting the entire thread, which sounds like is something you actually don't want happening. This is why they need that permission.

Thanks for the explanation. I want my moderators to be able to approve and deny. Currently they only have a 'approve' option.

Oh wait. I see now. The 'approve' option leads to a 2nd screen with both options. This is confusing because moderators do not click the approve link when they want to deny. Why not make a disapprove link in the drop down?

Separation performed for 4.0.0 Alpha 1. There are now 2 new inline moderation actions 'approve' and 'deny' which both post to 'doapprove' but which have different confirmation text and options.