Nix does seem like a great package manager. If I understand it correctly, a
    system using Nix wouldn't have the usual directories like /bin but I'm sure
    that programs with hardcoded paths could be fixed.

(We don't call filenames "paths".  See the GNU coding standards.)

With Nix, how does the shell search for an executable?

Can we rig up a virtual directory /bin that would appear to contain
the files it ought to contain?

    If you're not familiar with Nix, the developers have a video online:
    http://blip.tv/file/4726612

Can that be viewed without running nonfree software?

--
Dr Richard Stallman
President, Free Software Foundation
51 Franklin St
Boston MA 02110
USA
www.fsf.org  www.gnu.org
Skype: No way! That's nonfree (freedom-denying) software.
  Use free telephony http://directory.fsf.org/category/tel/