I can get podcasts onto my ipod shuffle, but they don't necessarily play in the correct order nor does it keep track of where you are in an episode if you sync before completing an episode (either on the ipod or on the Mac).
After reading some of these replies, I rebooted my Mac and it worked.
Make sure you have podcast episodes in the Podcast app.
Open the ipod shuffle in a finder window and click on the Podcast tab to see what is on it. If you are in the middle of an episode it will sometimes give you a check box to keep it loaded on the ipod, but it will revert to the start of the episode. Back in the Podcast app, sometimes the episode will disappear from the Episode list even if not finished (it gets marked as "played" even though it is not done.)
I have reported these issues to Apple several times using the "Report a Concern" feature under the Help tab in the Podcast app.