Icosphere smoothing problem on 2.6?

Screwing around in the new version of blender, I make a checkerboard plane, and a smooth mirrored icosphere. Everything works fine.

Then I make a bunch of duplicates with shift+D, and now some of them look like this? They’re all using the same material, of course.

Source file.

Two or more objects occupying the same space (delete one of them) or duplicate vertices (W / remove doubles)

That worked, thanks.