What is the danger in including the same JavaScript library twice?

The browser will cache the file, downloading it only once. It will be executed more than once however. So the performance impact is negligible, but the correctness impact might not be.

Depending on the library, including it more than once could have undesired effects.

Think of it like this, if you have a script that binds a click event to a button, and you include that script twice, those actions will be ran twice when the button is clicked.

You could write a simple function that you call to load a script and have it keep track of files that have already been loaded. Or, I'm sure you could probably use a pre-existing JS loader such as LabJS and modify it.

You should take an approach I learned examining the source of HTML5 Boilerplate:

<script>
    !window.YAHOO && document.write(
        unescape('%3Cscript src="/js/yahoo/yahoo-min.js"%3E%3C/script%3E')
    );
</script>

I don't use YUI, so replace !window.YAHOO with whatever global YUI uses.

This approach will only load the library if it does not yet exist in the global scope.