I added a message from Apple Mail to database (DTPO2), where it went to folder called “Today.” I have been unable to move it from that folder to another one, either by dragging or command. Is this a known issue?
“Today” is a smart group that lists the content you have added today. Obviously, you cannot move something out of that group. But those items will be gone tomorrow. They will be listed in the “Yesterday” smart group. 
You will find the item you are looking for elsewhere in your database. Try a search for it, based on Name, or a word or phrase in the content.
Or, in the Today group, select that item and press Command-R (the Reveal command). That will shift the view to display the “filed” location, and you will be able to move the item to any group location you wish, from that view.