Magento 1.9 – Fix Uncaught TypeError: Cannot Read Property

I think you are missing some DOM elements and/or ids. For example in your checkout there is not element with ID: 'billing-buttons-container' or 'shipping-buttons-container'. I think these are the elements that are null when trying to set some properties on them.
You might be missing other elements also. I recommend to compare your checkout templates with the default templates.

I'm guessing above code is jQuery. In that case you'll need to wrap the code to prevent issues with the Magento Prototype library

<default>
<reference name="head">
    <block type="core/text" name="your.block.name">
       <action method="setText">
          <text><![CDATA[<script type="text/javascript">
    jQuery.noConflict(); // prevent conflicts with prototype

    (function($){ // and wrap it
    $(window).load(function(){
        $('.HoverAlls_Caption').HoverAlls({
            "coords":"0,100||0,75||0,100",
            "text_coords":"0,50||0,5||0,50",
            "speed" : "220,220",
            "text_speed" : "400,200",
            "opacity" : "0,1",
            "link_control" : "false,_blank",
            "bg_class" : "captionBackground",
            "text_class" : "captionText"
        });
    });
    })(jQuery);
</script>]]></text>
       </action>
    </block>
    </reference>
</default>