The problem appears to be in an OS X framework we use to display the preview images. If the image is corrupt, the preview function winds up crashing Name Mangler. The workaround: Open Name Mangler's Preferences, click on General, uncheck "Show icon previews for image files."
Name Mangler will now be able to rename the image files. You could then revisit preferences and re-enable the icon previews, if you want to—at the risk, of course, of a future corrupt image again crashing Name Mangler.