I've listened to podcasts using the "recently added" playlist since I began using my first ipod nano in 2005. It worked beautifully, at least for me. I was a little apprehensive when apple came out with the podcasts app but since my playlist was still there, I decided it wasn't too bad. And then I updated to ios 7 and realized my "recently added" playlist was no longer updating. After some trial and error, I realized that I could get it to update but it is a little annoying. First, I'm running ios 7 on an iphone 5 and don't know whether the bug is effecting all phones. Secondly, I contacted apple and they assured me they know about the bug and are working on an update. Here are the steps.
1. Close the podcasts app (make sure it is not in the app switch list when you double push the home button)
2. Completely shut down your iphone by pressing the power button for a few seconds and then sliding the shut down where indicated.
3. Once it is shut down, reconnect to your computer allowing itunes to start and sync your phone.
4. After synced, open your podcasts app and your "recently added" playlist should have updated.