I normally use webmail to check for my mail and every once in a while i download it to another computer for permanent storage. This means e-mails are stored on the POP3-server most of the time, but although they are marked as read, plus keeps telling me they are new. Because the read-flag only could be set by (owner) interaction, is it possible that Messenger Plus does not speak about those e-mails?

The problem comes from the POP3 server. When Plus asks it for the number of unread emails it answers the total number of emails in your inbox folder. You (nor Patchou) can't do anything to solve this, however you can make new folders for read messages. They won't be counted.