When I right click the image, I get the pop-up dialog box as I should, but when I click OK to dismiss it, I get the very right-click menu that I would have gotten had the script not been present in the code. That is, I get the right-click menu for images, the one that contains the command "Save Image as..."

I posted this over in the Dynamic Drive scripts help forum: http://www.dynamicdrive.com/forums/showthread.php?t=5614 (see there for more details), and jscheuer1 determined that it depends on the position of the OK button when you click it to dismiss the dialog box. If it's over an image, you get the Images menu; if it's not over an image, you don't. He wrote an improved script that actually works. Dynamic Drive might want to consider using his script instead of the one currently presented on the site.