Now, I don't know if you knew this already or if you've seen the info floating out there, but Facebook has officially started rolling out the ability to add your podcast directly to your Facebook Page. I just added our church's podcast to our Page and while it does appear (only on the mobile app), I haven't been able to successfully play an episode yet. I also added the Digital Ministry podcast to my personal Page, but it only grabs episodes for the past two weeks and it'll probably be a few days before the next episode of that comes out. (wink, wink)
I like the idea of Facebook doing this, especially since so many church members are already on Facebook and, for many small churches, it tends to be the main digital hub that we have. For us to us a podcasting service to host audio versions of our weekly sermons and then to have Facebook automatically distribute them for us, this becomes a layer of convenience to help our digital ministries that we should not overlook.
As far as our podcasts not playing at the moment, I do have a support ticket in with Facebook to get some information and I'll update here when I find out more about it.
If you'd like to go ahead and link your own podcast to your Page, check out this article from Facebook. And if you'd like to get started hosting your own church sermon podcast, I highly recommend using Anchor as it's free and easy and what I have moved all of my podcasts over to.