I must have missed something,
Yes, most definitely you have missed something.
I don't have a crystal ball. Please start a conversation with me and provide me an a Admin Account (with full Admin Permissions) so that I can troubleshoot your issue with permissions myself.
When your Permissions are set correctly, this is what things will look like...
On a Showcase ITEM Page, at the base of the Content, you will see the Standard XenForo BYLINE with META Controls (name, date, and links like EDIT, DELETE, UNDELETE, REPORT etc). Every link is controlled by permissions. You will also see that there is a sidebar block named "Showcase Tools" This block displays to users that have Permission to do specific tasks (like feature, set cover image, reassign, approve/unapprove, edit, delete etc). This block is also controlled by permissions.
On all of the ITEM listing pages, there is also INLINE Moderation (allowing you to perform bulk actions). You can see here that when permissions are set correctly, that all the tasks.
Now on to USER REVIEWS....
Pretty much the same thing with User Reviews. At the base of EACH user review is the XenForo standard byline with meta controls. The red arrows point out the meta control links. You can also see that there is also INLINE moderation checkboxes available on ALL User Reviews.
Here you can see the User Reviews INLINE Moderation Actions.
now onto COMMENTS...
Comments have the same exact controls as User Reviews, so I am not going to explain that again.
Setting Permissions.... Showcase has a super nice Permissions Interface that lets you set Showcase Only Permissions (instead of using the core xenforo interface which lists all core xenforo permissions along with all permissions for every addon). To access this, you click on the Showcase Permissions menu option on the Applications tab. It will then list all of the User Groups you have in your system (I only have 5 on this development instance). You then click on one of the user groups and set the permissions for THAT user group. You'll need to do this for ALL your user groups. You CAN use the other system as well, this is just a lot easier since its only showcase permissions that will be displayed (XenForo Media Gallery uses this same system).
This is what the Interface looks like. There are TWO Tabs. One of for setting User Permissions and the other is for setting Moderator Permissions.
NOTE: Moderators and Admins are USERS, so you have to set User Permissions for them too. User Permissions are simply permissions that are NOT considered 'Moderation type' permissions (like being able to RATE an item).
I added a bunch of red comments on this screen shot to point out various groupings and type of permissions that are vital to actions that control whether the viewing user can MODERATE and what actions they can MODERATE. Some Moderator actions are LINKED... ie, in order to access the Moderation Queue, the Moderator needs EDIT, DELETE AND APPROVE/UNAPPROVE (for all 3 types, ITEMS, COMMENTS, REVIEWS).
