There is currently no ability to delete the logs for failed emails which are accessed from Contacts > Filter By > With Email Delivery Problems. For example, there was an email that was not sent because of an error with the receiving email. That was sorted but in order to remove the log of the event (which was 2 years old when I came on), I had to send a manual email to the contact. I should have been able to just delete the old log as the Admin.