Google Webmaster Tools 404 URL errors

Google crawled my site and listed every media category URL as a broken link (404) error.

Now I tried checking the links and I can see them when I’m logged in – but I can’t seem them when logged out.

Is there a way to make these URLs publicly available so Google and other search engines can see and list them properly?
Or otherwise hide the URLs so Google and other search engines don’t even crawl them at all?

Either solution would be ok for me.

Thanks for any help.

Here a sample URL:

http://www.thesandyfeet.com/media_category/yosemite/page/2/

https://wordpress.org/plugins/wp-media-library-categories/