OK, this one is in the 'painfully obvious' category now that I know about it ... but just in case I wasn't the only one...
When you are viewing movies in QuickTime's full screen mode, you can move the controls box just by clicking and dragging it. I just never thought of a transparent overlay as a window, so I hadn't ever tried it.
For those of you that don't have Quicktime Pro (I do), there is also this hint (and associated comments) on how to watch movies in full screen mode even if you haven't bought QuickTime Pro.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20070328011526590