[berkut]

They're using uni-directional path tracing - if they're using PRMan 17 (Which I think they were), it'll probably be unbiased like with Arnold. So it's unbiased, but unidirectional, unlike LuxRender's MLT (two-way path tracing).

PRMan 17's a fairly good raytracer now (Arnold was giving PRMan a bit of a kicking in this department over the last two years).

All on the CPU - there's no way GPUs can cope with the size of textures and geometry feature films need to cope with (up to 200 GB of textures and Geometry in some of the complicated scenes) - there's no way that's fitting on a GPU.

I don't know what Pixar have, but SPI (who use their own version of Arnold) used to have quad socket i7s, so 64-thread machines with 96 GB of RAM two years ago - some of the more complex frames were taking +30 hours at 2k.

[ginko]

Combining bi-directional path tracing and ray differentals(needed for texture filtering and geometry subdivision) doesn't really work well together at the moment, sadly.

[berkut]

Ray differentials are just two extra rays one pixel up and right of the main ray to give the ray width. It's pretty trivial to keep them up to date with the main ray at surface intersections (it's technically more work, sure), but it's doable, so I don't see a problem with it.

BDPT is more concerned with the surface area of meshes and solid angles of hits, so that the light path vertex weightings can be accurate.