This was added, amongst other changes, in section 1.E.iii:
You represent and warrant to Yahoo! that:
(a) you have the right to use, reproduce, transmit, copy, publicly display, publicly perform, and distribute any content in or made available to Yahoo! and Yahoo! users by your use of the Yahoo! APIs in the manner contemplated under this Agreement, and that use by Yahoo! or others of any such content via the Yahoo! web service or API shall not violate the rights of any third party (e.g., copyright, patent, trademark, or other proprietary right of any person or entity), or any applicable regulation or law, including but not limited to any export, re-export, or import laws and the laws of any country in which your content or service is made available; and
(b) if you submit or permit the submission of your or your users’ content or activity through or into a Yahoo! web service or API, you also grant the following perpetual, non-exclusive license to, use of, and rights to your or your users’ content or activity to others (such “others” may include but are not limited to Yahoo! users): (i) to access, distribute and/or display your or your users’ content or activity; (ii) the ability for Yahoo! registered users to rate, review, comment on and tag Your Content; and (iii) the ability to access, reproduce, distribute and/or perform your or your users’ content, activity, or information via Yahoo!’s web service APIs or via RSS or any similar XML or related feeds both on and off Yahoo!-controlled web sites.
It's the bit of the license that says if you submit content to a Yahoo! API, you grant the rights to anyone to reproduce that content wherever they like. A lot of sites' APIs include this (though often they make clear that you retain the rights to the content), but Yahoo! didn't, previously.
Another restriction is found in section 1.G.iv, but has been there since the start:
YOU SHALL NOT [...] Sell, lease, share, transfer, or sublicense the Yahoo! APIs or access or access codes thereto or derive income from the use or provision of the Yahoo! APIs, whether for direct commercial or monetary gain or otherwise, without Yahoo!'s prior, express, written permission.
i.e. even any indirect "commercial or monetary" gain—which seems fairly broad—prevents you from using the API.