Hi,
I was having trouble getting the web part to work properly as well (already having installed the SmartTools.Query setup and enabling it in the Site Collection feature). But found a hack fix for the Accordion.
First I downloaded the "/_layouts/jQueryUI/ui.core.js" and "/_layouts/SmartTools.jQuery/jquery-1.3.min.js" from SharePoint server (where the jQuery files were installed). I then uploaded them to my "Site Collection Documents" library of my top level site.
I then navigated to the page that has the Accordion web part on it. I created a Content Editor Web Part (right above the Accordion web part) and added the following lines to it's source:
<scripttype="text/javascript"src="/SiteCollectionDocuments/jquery-1.3.min.js"></script><scripttype="text/javascript"src="/SiteCollectionDocuments/ui.core.js"></script>
This caused the web part to start working. My thinking is that there is some kind of bug with using the /layouts/ path for executing the js files? Maybe the file's content type is not being sent to the browser properly and the browser thinks it is an unknown file type? Could it have anything to do with having SharePoint SP2 installed (maybe it worked in a pre-SP2)? I don't really know though.
Anyways, the disadvantage to the above method is that you have to include those files for each page you need the web part on (or place it in a custom master page). Hope this helps everyone until a proper fix can be found.