I had the exact same problems as everyone else here. The Podcast app would crash at various times, or hang and say it was rebuilding the library. Then I found that most of the native iOS apps weren't working, with Photos, the App Store, and Facebook crashing instantly, and Messages either crashing or freezing. Even Settings would crash on me and I would get error messages trying to restore from backup from my computer.
But after a hard reset, I was able to get back into Settings and turn off all of the options in the Podcast app. That seemed to stabilize Photos. I deleted a bunch of old photos, which allowed me to open Music and delete a bunch of old songs. I have both backed up, so I can go back and retrieve them again. But after clearing a bunch of space off the phone (even though it said I had lots of space available), most of the apps started to work again.
After one final reset, Messages started working again, and the Podcast app was up and running. All without having to reset or lose any actual data. It may not be a solution for everyone, but it may be worth a shot for some of you.