1. I am listening to podcasts, not song tracks. I saw a similar-looking problem reported for the 4th generation shuffle, so the problems might be connected to a software update.
2. I uninstalled iTunes completely and reinstalled it--the problem persists.
3. The tracks that the shuffle reports as "heard" are at the end of the list, not at the beginning. Right now, the list is organized by numerical order, and iTunes is counting tracks as played from the end of the list instead of from the beginning.
Looks like a bug in iTunes 10.6.1 to me.