<p>I have to preface this with the fact that I love jQuery as a JavaScript language extension and YUI as a rich set of free controls.  So here is my question, is there going to be any problems down the line if I mix jQuery and YUI together in an MVC app I am working on.</p>

<p>I want to use jQuery for the heavy lifting on the DOM and I want to use YUI for the rich user control set.  This is an internal application and will never see the light of day outside of the organization I work for.  </p>

<p>If anybody has experience with mixing these two frameworks I would love to hear what your experience has been.</p>

Speaking from some experience in developing a small tool myself, I've used YUI's rich control set with Prototype for DOM manipulation in the past and experienced no issues. Admittedly, this was a small tool that didn't use a wide array of the controls.
Even so, I'm always hesitant to use multiple frameworks on my web projects; however, if you're only using jQuery's DOM functionality and YUI's control functionality, then I think you're fine - there's not really a conflict of interest there. Plus, with jQuery's noConflict() mode and YUI's namespacing, the two frameworks really shouldn't trump one another.