A Work arround for this is:
- As the slider is actually not working by default just don't call anything at start 
- Create a - JavaScriptfunction that will set the value of the slider while the mouse is  being held down inside the slider.
 
- You need to make the ui-slide-handle return a reference to its parent while is being helddown 
This solution works in all major browsers:
$(function(){
  $('iframe').ready(function(){
     var $document = $('#result iframe',$('#main').contents()).contents();
     $('.slider',$document).slider({
          //Prevent the slider from doing anything from the start
          start:function(event,ui){return false;}
     });
     $(document).mouseup(function(){
         $('.slider,.ui-slider-handle',$document).unbind('mousemove') 
     })
     //While the ui-slider-handle is being held down reference it parent.
     $('.ui-slider-handle',$document).mousedown(function(e){
        e.preventDefault();
        return $(this).parent().mousedown()})
     //This will prevent the slider from moving if the mouse is taken out of the
     //slider area before the mouse down has been released.                
     $('.slider',$document).hover(function(){
        $('.slider',$document).mousedown(function(){
           $(this).bind('mousemove',function(e){
                //calculate the correct position of the slider set the value
                $(this).slider('value',e.pageX*100/$(this).width())
           });             
        }).mouseup(function(){
             $(this).unbind('mousemove');
        })},function(){
        $( '.slider',$document ).unbind('mousemove'); 
     })          
    })
    });
The solution link:
Solution