The same happened to me, but the below answer is a temporary fix and it worked for me:
Answer courtesy of "Mike" on Yahoo Answers:
I have same version of OSX and Safari and had same problem. It appears that Yahoo mail currently has difficulty with Javascript. To get emails working again, I went to Safari\Preferences and took the check mark off "enable JavaScript". Then close Safari and restart Safari. Go to your Yahoo email and log in. You will get a message that your JavaScript is not turned on but click on the link that says to go to Yahoo mail anyway. Then email worked for me. You may have to enable Javascript for other internet websites. If you clear your cache or cookies, you will need to repeat the process of disabling Javascript. Maybe someone else has a better way of getting Yahoo email but this seemed easier than loading a new version of OSX and Safari. Hope this helped.