Can anyone give me a mapping of the buttons on the Zune to the mappings in the GamePadState object?  Also is there any official Zune specific documentation other than the FAQ?

Play/Pause is the B button.
Back is the Back button.
The center button is the A button.
If you have a generation 2 device with the touch pad enabled, you can tell if the user is touching the pad by querying the LeftStick button. You can also get the touch position as the left thumbstick.

Also I have made a wrapper for the input to make things easier if you want: http://xnawiki.com/index.php?title=ZunePadState. The wrapper also allows you to get input about flicks and taps on the pad.

There is no official documentation because it's just a CTP. They will undoubtedly have more documentation when they actually ship the final version.

Thanks for the info!

One more thing, how are pressing on different parts of the Zune Pad handled?  Does clicking on a certain part trigger certain button presses, or do you just get the A button regardless and then check the left thumbstick value to see which direction?

Oops, I forgot to mention that. You can access Up, Down, Left, and Right using the game pad's DPad input. This is the only option for generation 1 devices, so you might want to keep that in mind when making games. Generation 2's have both the left thumbstick and DPad available to them.

There are also some minor input issues with the gen 2 device. The entire touch pad is a single button so DPad presses are sort of "emulated". When you press the button, the hardware (or the framework) determines which spot on the pad you are touching and uses this to choose which DPad button (or the A button) you wanted to press. This has the down side that if you have two fingers on the pad and click down, the button may not register correctly. It's another thing to keep in mind when working with it.

The 2nd gen player also supports left stick press and left shoulder button.

ms-help://MS.VSCC.v90/MS.VSIPCC.v90/MS.XNAGS30.1033/XNA/UsingZune_Zune_Programming.htm

I knew about the left stick press (like I mentioned above, that tells you if you are touching the pad), but I didn't know about the left shoulder button. For those who don't want to look it up, the gen 2 player flags the LeftShoulder button as pressed when you click anywhere on the zune pad. So you can get a DPad direction and LeftShoulder at the same time. Could be useful for a game that just needs it to act as one input.