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.
Best Answer
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.