How to view all the downloaded podcast episodes on the iPhone?
It's been a while since this question has been asked. As of now, you can do it like this:


Click on "Library" in the Podcasts app.
Click "Edit" in the upper right hand corner.
Tap the circle next to "Downloaded Episodes" to check it.
Click "Done". You can now see the "Downloaded Episodes" option below "Library" text (under "Shows" and "Episodes").


This section contains only downloaded Podcasts.