This is partly a bug, partly a feature (perhaps?)...
If you have the Spotlight search results window open, but in the background, you can bring it forward by pressing (by default) Command-Option-Space. This not only brings the window to the front, but also hightlights the search term(s) in the Search field so you can type over them and run a new search.
But, if you press (by default) Command-Space instead, which displays the Spotlight menu, this also brings the Spotlight search results window to the front. While the search string in the window is highlighted, it is not active; the cursor is in the Spotlight menu search field.
But here's the bug: normally, if you press Command-Space to display the Spotlight menu, clicking anywhere else (in another window, on the Desktop, etc) makes the Spotlight menu fade away. When the Spotlight search results window is visible, however, clicking anywhere else takes you to that window, but the Spotlight menu remains visible. To get rid of it, you need to click in the search field, then press Escape. However, if you click in the Spotlight search results window, this makes the Spotlight menu go away.
You can use this glitch to actually run have two Spotlight searches active at once, as seen here:

Mac OS X Hints
http://hints.macworld.com/article.php?story=20051209013955751