iTunes app on iPhone won't download podcasts
If I browse podcasts in iTunes on my (iOS 5.1.1) iPhone 4, most listings of episodes don't even fully load, with the download buttons (or sometimes the entire listing) failing to render. The exact same podcasts on my wife's iPhone 4S on the same wifi network work perfectly.
There's almost 20 GB of space available in my iPhone, and I've tried ending all apps & rebooting the phone multiple times.
I feel like I helped my brother through something VERY similar involving downloaded/purchased music -- and the only thing we found that fixed it was a complete restore from his most recent backup. I surmised that it was something related to a horked cache file or setting at the OS level.
The other thing that it might have been related to was wifi syncing/backup; we also turned that off, if I recall, and it wasn't until it was turned off that things returned to copacetic.
This is all fuzzy memory from months ago, though, so YMMV.
I had a similar experience and decided that Apple wasn't resolving the post-iOS 5 & iCloud issues with podcast support as quickly as I hoped. I did some research, and switched to Instacast on my iPhone for audio podcasts, and Instacast HD on my iPad for video podcasts.
This switch addressed all of my issues and created very few. The cost was minimal and I got several additional features that I consider useful.