It would be very helpful if the app automatically marked listened episodes as listened, and the UI should have a filter option to show only unlistened episodes.
Should be a way to manually mark an episode as listened or unlistened too.
We've now shipped this.
Individual podcasts can be marked as "listened" manually:
You can filter a podcast by its listened/unlistened episodes:
And finally, when a podcast episode has completed playback, this will also be marked as listened.