This app lets you manage podcast subscriptions. It will keep track of episodes you've downloaded and delete them when finished. I'm just doing this out of my own interest and not looking to make money so there aren't any ads.
Instructions: You can use the search function to find podcasts from the app store to subscribe to. All of your subscriptions will appear on the main screen. When you view a podcast, all undownloaded episodes will be white, and all downloaded ones will be listed in blue. When you finish an episode, it's marked as "finished" in the database automatically and deleted. You can download it again by switching the view selector from "all unplayed" to "finished".
Also, you can long-tap an episode to see a description.
Contact me with any suggestions/bug reports, and I'll try to fix them asap. Enjoy!