Shader shows black lines from occluded object

Please look at the embedded image to see the artifact. There are black lines bleeding through from the occluded object underneath. Is there any way to avoid this artifact?

It used to be that this artifact would show up on PC and not Android/OUYA, but with the upgrade to Unity 4.5 it now shows on both.

I have attached the shader being used. [28327-lightpiecesshader.zip|28327] It is simply the builtin blinnphong shader with one line added for energy conservation, and every mode that is not using directional lightmapping stripped out. The other change is a -2, -2 Offset parameter, to remove problems with z-fighting between various layers of the game.

Removing the offset parameter fixed this.