Try the steps below, worked for me.
1) Delete the podcasts application from your iPhone and be sure that it will not be loaded from iTunes again. (press on podcasts app until there is a minus sign for delete visible).
2) Shut down music, if it is open (double table the home button and then scroll to music and press the minus sign).
3) Power off the iPhone (hold down the top button to until a message that says slide to power off).
4) After the power off, hold down top button until apple logo appears and iphone starts.
After the above steps, podcasts were back in music and could be used with music playlists (as before).
I got these instructions for other BBS, tried them and they worked for me.
I tried this, and while my podcasts are in my Music app now, I still cannot make playlists that include podcasts. I can play each podcast individually from the Music app, but I would like to make a playlist of several podcasts to play in the order I want. And sometimes I like to mix songs and podcasts on one playlist. It used to be so easy to create exactly the playlist I want, with the content I want. I wish I did not have to play podcasts individually because sometimes the shows I want to hear are shorter than my commute.
When I make a playlist from my phone, I click the "+" button at the top left, the Podcast tab goes away. When I am not making a playlist, the Podcast tab is back to the bottom of the screen in the Music app. So frustrating!
I may be asking too much, but I would like to be able to make my playlists on the go, from my phone, instead of having to wait until I go home and open itunes on my computer to create the playlists to synch. There are weeks when I just don't have time to deal with itunes on my computer and I would rather make my playlists at the time I want to hear them, even when I am away from home.
Any help with this would be great.
I want to do the same thing, and there is no way to do it. I've tried every suggestion on this list. They're helpful for other things, but not for creating playlists of podcasts directly on the phone. I have the same issue with podcasts that are shorter than whatever I'm doing. There is currently no solution. By participating in this discussion group, we are not accomplishing anything other than venting. Apple doesn't read these comments, as far as I know. And while they've fixed other things in iOS6 they haven't addressed the podcast issue. They clearly think there's not enough of us to matter. If you would write to Apple directly, it might help.