404 to sites/default/files/css/,
Assuming everything is using proper Drupal methods for attaching stylesheets (.info, drupal_add_css, $foo["#attached"]["css"], etc), I think it is impossible for core to create a bad link to a file.  Still, it would be worth it to search the code for "drupal_add_css" and "#attached" to see if there are any problems.

I think there are two possibilities here.

One could be a JS library dynamically attaching a stylesheet to the page.  Unless you are doing this yourself, I don't think this is a likely culprit.  Most of the libraries that do this (eg, jQUery UI) are rather well tested and I doubt would do this.  Stranger things have happened, though.

The other possibility is a bad url() reference in your CSS for a font or background image.  Search though all of your CSS for "url" and see if you have any problems.  Validating the CSS couldn't hurt, either.