Okay after a deep investigation my conclusion is as follows:
* Media Browser works ok with javascript
* Media Browser works ok with jquery
* Media Browser works ok with jquery served from another domain
* My issue: Media Browser cannot deal with the microsoft cdn version of jquery (<script type="text/javascript" src="http://ajax.microsoft.com/ajax/jQuery/jquery-1.3.2.min.js"></script>)
Regular desktop browsers work with all of the above (including firefox, ie, chrome). Therefore I recommend if you do want to use this use the google Ajax Library API at http://code.google.com/apis/ajaxlibs/documentation/
I'd still like to see documentation, a script console and debugger for the media browser however.