The difference is coming from this function in your megamenu plugin:
Code:
addshim:function($){
$(document.body).append('<IFRAME id="outlineiframeshim" src="'+(location.protocol=="https:"? 'blank.htm' : 'about:blank')+'" style="display:none; left:0; top:0; z-index:999; position:absolute; filter:progid:DXImageTransform.Microsoft.Alpha(style=0,opacity=0)" frameBorder="0" scrolling="no"></IFRAME>')
this.$shimobj=$("#outlineiframeshim")
},
which, in the case of https, is appending an iframe onto blank.htm. This doesn't exist, so you get the 404.