Apple: The Fix is In
Responding to our request for more data, Head-Fi Forum member "Nine" passed along some measurements that showed both a 500mV steady-state DC output, as well as a sporadic pulse signal. He wrote, "My theory on this (mind you, this is only a theory) is that the 1.1 firmware is not properly powering down the DAC."
Apple has released a v1.1.1 version of its firmware, saying only that it includes "bug fixes." Members of various Apple Forums are reporting that v1.1.1 does indeed solve the hiss, hum, and other noise problems introduced in the v1.1 update. Interestingly, some users also report that older versions of the firmware would power the system up when headphones were plugged in—a feature that no longer seems to work.
Since Nine told us he had measured very small amounts of DC offset with the v1.03 firmware ("nowhere near what I was seeing with 1.1"), this suggests that iPod Classics were never fully powered off, which would also explain the frequent complaints about battery-charge life. The firmware update should address that, as well.
We were alerted to Apple's release of the bug fixes by an email from Stereophile reader Jimmy Olson, which is just one more reason why we love the interwebs: people share information. Thanks Jimmy.