You have several javascript errors on your website:
Uncaught ReferenceError: google is not defined
on that line:
google.load('search', '1', {language : 'en'});
Uncaught ReferenceError: toggle is not defined
on that line:
toggle('status',1)
And:
Uncaught ReferenceError: MenuMatic is not defined
on that line:
var myMenu = new MenuMatic();
Because of these errors, the javascript which loads the state dropdown cannot work properly on FF.
I would recommend to either ask the support of MenuMatic to help you fix the javascript errors you have or use another suckerfish menu module as it apparently comes from that.
Once the javascript errors on your website will be removed the dropdown will work properly.