Thanks for the update. Aside from deleting and re installing the app, you could next try deleting your downloaded podcast episodes and re download them, to see if one of the episodes has gone wonky and is crashing the program. If the issue persists, the next best thing to do would be to delete the app itself, then re install it.
http://support.apple.com/kb/TI135
To delete an app you downloaded from the App Store, touch and hold its icon on the Home screen until it starts to jiggle. Tap x to delete.
If the issue is still not resolved, then the next thing to do is back up your device to iTunes:
iOS: How to back up and restore your content
http://support.apple.com/kb/HT1766
And restore it from your backup with this article to delete the current iOS installation and install a fresh copy.
Use iTunes to restore your iOS device to factory settings
http://support.apple.com/kb/ht1414