Currently Being ModeratedMar 27, 2013 7:39 AM (in response to nickb23)
One or both of these may help you.
(1) Perhaps you installed some additional software on your Mac mini to control your Logitech?
If so, that software's driver may be overriding the Mac OS X webcam software and causing trouble with the "fixed focus and exposure and white balance" requirements for using Photo Booth's backdrops shown in http://support.apple.com/kb/PH5610
As one example, Logitech's http://tinyurl.com/ckfesn7 Troubleshooting page advises that their software may limit compatibility with some applications, Photo Booth included.
If you have installed any software beyond that automatically installed by OS X, follow the supplier's instructions on now to uninstall it, restart your Mac, and test again.
(2) Your problem can also be caused by small, even tiny, movement of your camera:
Movement in the camera's background field of view, even air moving pictures or curtains behind you, can also cause this.
Make sure everything is absolutely still, restart, and test again.