Right now on mobile devices, once you're done listening to a podcast, nothing happens. There's no signal that you've already listened to it or anyway to mark it as listened to except for clicking on it and dragging the time bar to the end of the episode. On the computer interface there's a little blue bar that shows you if you've listened to it or how far into it you are, but there's also no way to easily signify if you've already listened to the episode. There should be some way, whether its a blue wheel or another visual form that shows people if they've listened to a episode or not, and there should also be a way to click the control for an episode and mark it as already listened to.
Updated on 2019-05-23
This has now been implemented. You can find the 'Mark as Played' button by clicking the three dot menu next to Podcast episodes on Mobile.
You can also check out how much of a show you've listened by checking out the green progress bar and time indicator. It'll say 'Played' once a Podcast is complete.