Muse has thoughtfully kept numerous copies of a site I've designed, and I want to delete all but the newest one; is there a way to do so from within the application so I can see the files' differences visually?
Muse doesn't keep or create copies of your sites. It has no such feature.
If you have copies or your site, you must have done it by yourself. Consequently you have to delete them by yourself.
By copies, do you mean the thumbnails that appear when you first launch Muse? These are just recent files. If you've overwritten, moved or deleted the different versions, it will ask if you want to remove the thumbnail when you click it. Otherwise, you can remove the thumbnails completely by going to File > Recent Files > Clear Recent. The list will start building again once you open your site(s).
Thank you, Mac and David.