Yahoo was contacted about this and they say it is a glitch, they have their engineer working on the problem. This has been happening to many of us while using the Classic Mail, since Yahoo has been upgrading the Classic and other sites, in the meantime, open the inbox, click View All Messages, then unread messages, if you have any late arrivals or in folders they will show. Otherwise it will clear on it's own. It did for us, it took a few days.
Just another Yahoo glitch It is one of many problems. Hopefully they will get it right soon. If all else fails go back to classic mail via this link. http://us.mg1.mail.yahoo.com/dc/optout?s… click yes when asked do you want to opt out. Hope this helps.
I don't think that you really can. Usually it shows that you still have mail in your inbox because you opened another window, and when you switch back to the first page, it will still show that you have mail.