It used to be if you had the item "checked" it would continue to play. Personally, I use the checkbox to track new podcasts that I then uncheck after I've distributed it to the desired playlist (I create one for each week since most of my podcasts are weekly and I'm usually a couple of weeks behind listening to them). But the actual function of the checkbox was to allow you to select which songs (items) in a playlist would be played. Interestingly, the checkbox had no effect on playist behavior when synced to an iPhone (though iOS 6 tries to force you to switch to the Podcast app that has its own deficiencies, like supporting playlists!).
I'm not sure how or why they screwed the pooch on this one, but I can't even drag the entire list to the "Up Next" list. It appears that the iTunes 11 and iOS6 designers simply don't understand podcast listeners (nor likely care about them either).
They're all checked....
The behavior has changed inexplicably in the past few weeks since the original post.
I did some experimenting before this and changed the "Media Kind" from "Podcast" to Music for a few of the downloaded podcasts. This worked but changed the location of the podcasts in the library, and they didn't roll off to the Trash after playback. So I trashed those downloads manually and went back to the "single play" downloads.
After a few days, the original "play through the list" behavior returned. Just as in iTunes 10. This lasted a little longer than a week.
Now the podcasts are downloading and stopping after a single podcast plays.
I've also noticed I can't add Podcasts to the "Up Next" list at all. This may be more indicative of the behavior as Music playlists see all the tracks in the "Up Next" queue by default.
Every now and then I come back to this issue and browse for solutions.
I found this post from a 2006 occurrence of the issue:
In iTunes, there’s a setting for each song or podcast episode labeledSkip when shuffling. (Select an item in iTunes, choose
File > Get Info, and click the
Optionsbutton to see it.) This option excludes the song from the playlist when you play it in with the shuffle feature enabled. By default, this option is turned on for every podcast you download.
You can turn off "Skip when Shuffling" on the Podcast Info (by selecting the podcast RSS line in the Podcasts) and turn off the default on a podcast basis.
I'll give that a try for a few days and post back later.