A number of people have been having this problem. I ONLY have it with my Yahoo account, not with my Exchange account. I never had this problem prior to the upgrade.
Essentially, if you delete an email without opening it, it shows up as unread in terms of a badge notification, but not in the "unread" section. It also doesn't show up in the trash. The only way to get rid of the notification is to go to the inbox, mark all as "unread", then mark all as "read". After a few minutes the badge notification will go away. This is really annoying and definitely a new problem with iOS7. I think some people are having this problem with Gmail and Hotmail accounts as well. This needs to be fixed....
Essentially, if you delete an email without opening it, it shows up as unread in terms of a badge notification, but not in the "unread" section. It also doesn't show up in the trash. The only way to get rid of the notification is to go to the inbox, mark all as "unread", then mark all as "read". After a few minutes the badge notification will go away. This is really annoying and definitely a new problem with iOS7. I think some people are having this problem with Gmail and Hotmail accounts as well. This needs to be fixed....