Podcaster will automatically download new episodes and deletes old episodes. This can be controlled with 2 settings.
"When new episodes are available...." setting
This is applied during a refresh for each podcast as Podcaster finds new episodes.
"Episodes to keep" setting
Old episodes are deleted from disk as a new episode of each podcast finishes downloading. That means that even if you have this setting set to "keep only unplayed episodes", played episodes will remain on disk until new episodes are finished downloading. The titles remain in the app for history purposes. You can hide all played episodes by using the 'Auto-hide played episodes' setting.
A few things to note, if you change either of the 2 settings, the settings are not applied until a new episode is found or a download has finished. Refresh and Download Queue cannot start if the app is in the background but will continue in the background for up to 10 minutes after it has started.
Also, Podcaster 3.7 and earlier had a feature called "Clean Disk" This deleted old downloads and removed the history. This was taken out for the sole reason that if you had all episodes played, then you ran a cleanup and all episodes got removed (including history), the next time you refresh that podcast, all episodes would be found and redownloaded again.
We hope this helps most users. Please post questions to the comments area.