How to delete multiple podcast episodes from iOS 6 podcast app?
The Podcasts app was updated for iOS 7 on October 22. I don’t think that this was a feature of iOS 6’s Podcast app, but if you are able to update to the latest version, there is an Edit button that can delete/mark-as-read multiple episodes or multiple subscriptions. (Assuming you’re not running an older device that isn’t compatible).

There isn’t a way to so multiple selects before a swipe to delete, though most apps have an “Edit” button to select multiple items before hitting the Delete button (as seen in Mail). In third-party apps, the interface depends on what the designer/developer built.