I have finally got to the bottom of this issue and reproduced the error.
On the site where this is happening, there is a login. If the user does not log in to the site, the live support runs through http or non-secure page. However, if they do log in, then the live support will run through secure (https) site.
We have set up the Operator's Picture URL to point to an image on the non-secure site. But when live support runs through https, it tries to add the non secure image to the secure page. IE8 warns the user about this and asks them if they want to display the non secure content. If the user clicks 'Yes', the error occurs.
To reproduce the error I downloaded Microsoft's VM image for XP & IE6. I then updated to IE8 which then gave me the environment the client had.
I have fixed this on our setup by setting the operator's image URL to point to a secure URL so IE doesn't complain even if the live support page is non-secure.
Can I suggest that CuteSoft modifies the error output. I personally don't want to spew out blocks of code to public clients. So I have changed the error to be a lot more user friendly, if anything else kicks off an event handler error.
Hope this helps anyone who has encountered the same issue.