Downcast or Pocket Casts are your best friends.
I can't understand why Apple didn't try to replicate how "Pocket Casts" works... This app is simple, yet powerful and beautiful...
Downcast isn't as beautiful, but is way more powerful/customizable. (Auto-download, podcasts/play position synchronization between iOS devices, etc.)
"Podcasts" is a disgrace... Next time Apple, I suggest you put less effort on the "bling bling / eye candy", and better efforts in the functionalities...
Pocket Casts has a beautiful "Artwork view" for podcasts, Downcast is more "classic" (list of podcasts with a small artwork thumbnail).
Both apps are great. Personaly I use Downcast, but I've been using Pocket Casts for a very long time too. Give it a try, there's a "lite" version for Pocket Casts, and both apps aren't very expensive
Some other good "podcasts" apps you may want to take a look at: Instacast, iCatcher! and Podcaster