Where did Mail.app just put my email? Mail.app seems built to punish us for not having inbox-zero.

I hear a chime telling me new mail has arrived, but with a list of mailboxes that look like:



how can I possibly tell which one has new new mail, as opposed to the old new mail? Or better yet, is it possible to make an email's newness expire after a certain period?
Create a Smart Mailbox with "Message is Unread" and sort it by Date Received. 
I have this setup as my default mailbox for processing my email. I also have the Mail.app dock icon badge set to point to this Mailbox so I can see how much unread mail I have, though in your case this won't be an advantage.

Pro Tip. Just mark all those messages as unread read. You're never going to read them.