I haven’t figured out what to do now that Apple has removed the built-in support for podcasts from the Music app. Now at version 1.1, Apple’s Podcasts app is still clunky and slow and doesn’t sync properly with iTunes. Downcast seems promising, but it doesn’t sync with iTunes, either. I like to use iTunes on my Mac to manage and subscribe to podcasts, as well as archive the good episodes. Plus, I’m suspicious that with apps that do their own downloading I will end up in a situation where I have no signal and nothing downloaded.
Update (2012-09-21): Christopher Breen:
As mentioned, if you’ve installed the Podcasts and iTunes U apps, that’s where you’ll find this content. However, if you haven’t installed these apps and you sync, within iTunes to your device, podcasts and iTunes U content, you play that content within the Music app. Just tap More and you’ll find entries for both kinds of media.
So that’s an easy solution, for now. Thanks to everyone who brought this to my attention.
Update (2012-10-05): Kirk McElhearn:
If you care about podcast playlists, it’s clear that the Podcasts app isn’t for you. But if you’re a casual podcast listener and just want the content, then subscribing to podcasts and downloading them from the Podcasts app may suit you. You may not like the interface of the Podcasts app, but it does an OK job with what it’s supposed to do.