Hi
It seems as if the Content Search WebPart is not functioning in SharePoint Online. I have no trouble adding the WebPart to a page and configure the query in the "Change Query" interface which is correctly displaying the results in the Preview pane as i build my query. The problem is that when the WebPart is saved and the page is published, the WebPart doesn't display anything, as in anything.
I did a bit of digging and the root cause is a feature, Search-Driven content (id: 592CCB4A-9304-49AB-AAB1-66638198BB58), thats not activated at the Site Collection. I tried activating that feature with CSOM but it fails due the feature not being installed in the farm. This post describes the issue http://corypeters.net/2013/04/broken-content-by-search-web-part/.
Other frustrated users
http://community.office365.com/en-us/forums/148/t/163145.aspx
Hopefully someone will fix this soon!