I got it working. Apparently is some kind of timing/order issue:
The new Javascript:
$(".edit").click(function(){
$(".math-tex").each(function(index){
$(this).html("\\(" + $(this).find("script").html() + "\\)");
});
$("#fullarticle").attr("contenteditable", "true");
CKEDITOR.inline('fullarticle');
});
$(".save").click(function(){
$("#fullarticle").attr("contenteditable", "false");
for(k in CKEDITOR.instances) {
var instance = CKEDITOR.instances[k];
instance.destroy();
}
MathJax.Hub.Queue(["Typeset",MathJax.Hub]);
});
However, you cannot edit/save multiple times. Try it, the second consecutive time that you press edit it will display really bad.