The class Fx.Slide , which was the problem initially stated, is part of the mootools-more.js library.
That library was missing from your page, therefore I have used jQuery Easy to add that library manually.
The issue is gone and your menus now seem to work as expected but I have not checked all of the checking pages of your site.

Note that the path is hardcoded into the jQuery Easy plugin and once you go live you will need to adjust the path (see the 'add scripts' section of the 'advanced' tab).

I have setup the plugin properly to just affect the checking part of the site. Other parts of the site should have a different treatment, since you have duplicates of libraries all over. But this is only possible to do with jQuery Easy Profiles.

I have removed:
/templates/no1_shopping/js/jquery/jquery-ui-addons.js
from the 'strip remaining scripts' of the plugin.

The dropdowns seem to work fine for me. If not please send me a screenshot of where I am supposed to look for defects.

There is no javascript error so therefore there is nothing more I can try with the plugin.