@dmk In the screenshot, it doesn't look like any of the folders have any unread messages (none of the folder names are in bold), which would be why there are no numbers to the right of them and why there's no total unread count to the right of "DMK_TROSE".
Click on the slanted wrench icon near the top right of Opera Mail and make sure "mark as read" is set to "manually" though. Otherwise, previewing a message will automatically mark it as read.