It seems to be an iTunes issue
Podcasts on my iPod touch worked fine while on a walk (no WiFi access) this morning. When I returned home and started to update podcasts, the app crashed on launch. Quitting the app, rebooting the iPod, deleting and reinstalling the app failed.
I then tried Podcasts on my iPad -- same problem. Turning on Airplane Mode on the iPad allowed the Podcasts app to run and to play podcasts, but soon as WiFi access was enabled, Podcasts app crashed.
After reinstalling Podcasts on the iPod touch, the app found every podcast I had subscribed to since the beginning of time (some of which no longer existed anywhere), and tried to download them. After many frustrating minutes, I was able to get the app to forget the ancient podcasts, and download the ones I wanted to listen to.
Well, it seemed to work, for a while. I just turned on the iPod, started the Podcasts app, and it crashed! After turning on Airplane Mode, the app works fine (other than the obvious issue of updating podcasts).