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So, when you open the app there are no podcasts shown in the left column?
Try pulling down your notification center and see if there are any related notifications. I can't think of what would be there, but it is all I can think of.
You can also go to Settings > Notifications, and choose the Podcast app to see what alerts and notifications are turned on. If nothing else you can just turn off the badge altogether.
I generally leave it off because, I really don't care how many unread podcasts are sitting in the app. I'll get to the them when I darn well feel like it, or not.