How can one filter out these annoying anonymous questions?

No, there is no way to filter them out, you are going to see them.

Reason for them, according to Yahoo...

Ask and Answer Anonymously

We know that there are some questions that we would rather ask and some answers we’d rather give privately. This is why we have launched the option to make your question or answer anonymous.

With this change, you can now choose to “hide” your profile from appearing next to the content after posting your question or answer. To make your question or answer anonymous, simply click “edit” and select the “make anonymous” option.

When you choose to make your question or answer anonymous, it will not appear in your history or in your network’s stream.

Note that making your question or answer anonymous will not have any effect on the content of the question or answer.

You will still get points for answering anonymously, and anonymous questions still cost points. Anonymous questions and answers are, of course, still subject to our Community Guidelines and any reported misuse of the feature will be acted upon.

No. Just like there is no way to filter out categories, there is no way to filter out questions, anonymous or not. The reason for this new feature, is that some users asked Yahoo for the obility to ask and answer anonymously, as some users may want to keep personal questions private.

Have a read of Yahoo!'s explanation: http://yahooanswers.tumblr.com/post/89850099282/ne...