new 4th gen. Won't advance to next podcast when I tap >>I

Each podcast is treated as a separate playlist by the shuffle. If you have more than one episode from the same podcast, you can select the podcast from the VoiceOver playlist menu, and then move back and forth between episodes of that podcast (like you would with songs on a playlist). However, of each episode is from a different podcast, you cannot, because each episode is on its own playlist.

The solution is to create a new playlist in your iTunes library. You can name it "iPod Podcasts" or whatever you want.

NOTE: To create a playlist, click the plus sign at the bottom of the iTunes sidebar. If the sidebar (along left side of window) is not visible, from the menu bar, under View, select Show Sidebar.

Add all the podcast episodes you want on the shuffle to that playlist. You mix episodes from different podcasts, and put them in any desired playlist order.

Select the shuffle in the sidebar. Near the top of the window, there is a bar of buttons starting with Summary. Click on Podcasts there. Check the box for Sync Podcasts if it's not already. At the bottom of the Podcasts screen, there is a list called Include Episodes from Playlists. Find that new playlist and checkmark it there. You do not need to select podcasts in the list above.

When you click Apply, the podcast episodes on the playlist (and the playlist) sync to the shuffle. Going forward, you can update that playlist in your iTunes library (add/remove episodes). The next time you connect the shuffle (or when you click Sync), it is updated with the same changes automatically.

When using the shuffle, with the power switch in the play-in-order (middle) position, use VoiceOver to select that "iPod Podcasts" playlist (not the separate podcast playlists). The podcasts should play in playlist order, and you can use the Next and Previous buttons to move between episodes (now that they are all on one playlist).