From a facebook standpoint I don't see this being feasible. Sure, you could attach the file id to the url fed to facebook to get individual like buttons when viewing, but the links back would be screwy and simply doesnt work because they need to be associated with a page.

I do however see the good possibility of rewriting the core Likes This block or my Enlil Likes This block (for modern c5 installs) to count likes by file id etc, thus allowing your site members to like individual images for instance!

EDIT:
On second thought, every image has a url. Allowing those url's to be liked via facebook should be fairly simple. Rendering social media on those url's is a different can of worms. It might be easier to set up a page type with composer and create simple pages for each image via file selector page attribute. In the end adding new images would be as simple as spending 30 seconds creating a new page. Then your fancyboxed images would have a page to call back to associated with those likes. Hide these pages from index and sitemap and watch your likes increase!

Thanks for your responses. It's not so much about collecting 'likes', it's more about allowing people to share and spread the word, without dedicating a page to each image. But I'll look into what you've said and have a play around when I get the chance.

Thanks for your time.