I Have the same problem. iPhone six plus. I was able to open the app and subscribe to some new hd video podcasts. Now the next day it won't open at all. Back to the home screen Every time I try.
I tried deleting all the data in storage in settings, and then turning the phone off for a while, but it didn't help.
The last time I tried that, the lock screen was frozen when I turned it back on; it wouldn't input my code or do anything or respond when I tried to turn it off!!! After a couple of minutes it started responding, phew. Then it went from 35% to 15% battery in a couple of minutes. This part is really weird and may have something to do with it being plugged into an Apple iPad charger that had kind of wiggled apart and was no longer charging.
P.S. Also the podcast app on my iPad is still working even though it also got upgraded. But the lack of full screen is really terrible. What happened to using the whole screen? And it's jumping around and playing too fast or freezing. I'll put the full screen issue in the appropriate thread, too.