I have a podcasting app suggestion: Instacast for iOS. Previous mobile podcatchers never did the trick, but Instacast has totally replaced iTunes for podcasts for me. It's very well done.
It does all the things I want--automatically downloading episodes, deleting them after they've been played, double speed playback, streaming episodes that are *not* locally cached, double speed playback working even with streaming (which I've never seen before), really good discovery of new podcasts, ability to import your existing podcast subscriptions (for all podcasts that are currently stored on your phone or iPod touch), and so on and so forth. And it has all of these features without being a cluttery mess.
ps: double speed playback in iOS is really 1.5 speed. I've heard some podcast hosts bitch about people using it for some reason. Talk faster and I won't, podcast hosts of the world. Or step it up to Scharpling level--I never 1.5x the Best Show.