Rotating Tweets (Twitter widget and shortcode) Not rotating

The normal cause of tweets not rotating is multiple installations of jQuery. That’s almost certainly the problem here, because jQuery gets installed twice – and the second installation overwrites the first one and all the plug-ins linked to it.

I suggest finding the plug-in or line of theme code that puts

<script src="http://code.jquery.com/jquery-1.7.1.min.js" type="text/javascript"></script>

onto the page at about line 83 of your homepage HTML and removing it.