I got it to work (sorry - don't have time to read through all the posts). You need to login to Yahoo mail from your desktop computer. Login (I needed to type a captcha-type code).
There are two verification security questions (like your pet's name, etc). You need to answer the two questions (if you already have them, you simply need to click "save without changes". I made sure I was using Yahoo Classic for both accounts I was having trouble with. This is what the "verification" message means.
Once your email is working correctly on your desktop, put the correct information into your iphone under settings > mail.
For some reason, this verification step didn't work unless I went to yahoo on my desktop.
My two cents:
Yahoo clearly didn't test this before mandating the verification step - or just put a crappy pop up without thinking about writing a FAQ or something. Apple should have addressed this somewhere. This whole thing killed about 2 hours of my time. This is why upgrading to a new iphone is always a pain in the ***.
Hope that helps.