After saving a query in the data explorer the web user gets no visual confirmation. The query page still looks the same, the URL in the browser's address bar is the same, etc.
However, if you search for your query and open it, the page looks a bit different. Only then I have no doubts the query has been persisted.
I was just creating my first query in the explorer and was a bit confused by this. Using
Chrome 11.0.696.68 (Official Build 84545)