Christos -- I've no strong opposition to your observations, but am not yet convinced these are bugs.
1. When editing a pending message and click on Save, the message is saved but then you are returned to the next message in the queue, not the one you were editing, resulting in having to go back in the pending message list view in order to approve the message you just edited. If you edited and saved the last pending message on the list you're instead returned to the list. It's almost like the Save and the Skip buttons are executed instead of just Save.There is a "Save and Approve" button in the Edit message screen. Why not use that?
2. There is an inconsistency in the availability of the "Reject" button and NM/Non-Member pending messages. In the pending list view, you can select that message and reject it. But if you click on the same message and go into pending message view, the "Reject" button is not shown.Should groups.io moderators be allowed to Reject (as opposed to Delete) a message from a non-member? Seems that most such messages would be spam, and rejecting it (which sends back a response to the sender) would just encourage more spam.
Having the same button appear in the pending list view makes sense because you might have other messages in that list that are from actual members.
I hope I'm making sense here!