I know this is a little bit old, but I started having this problem, and this thread was one of the ones that showed up. I believe I figured out a little bit more, at least in my instance.
I have a 5C, running the latest iOS, and the latest iTunes running on the latest Mavericks.
If you're having what I'm having, you don't see multiple copies browsing the iPhone Podcasts app; you only see the multiples when you go to "on this iPhone" in iTunes, or click the device in the sidebar. I had a similar issue; I was seeing something like a dozen copies of the same Freakonomics podcast, and often another one was getting added after I synced.
I checked my iPhone though - and I don't think there's actually mulitple copies of the file, despite what iTunes is telling me.
On the iPhone itself, go to "settings", and then "general", and then usage. This screen will tell you how much storage each app on the phone is using. If you click "Podcasts" on this list, the next screen will break down the storage used for each podcast. I took note of the size it was reporting for podcasts that showed duplicate copies in iTunes; and then added up the file size for the number of files that *should* have been on there. Three episodes should have been something around 80 MB, and that's exactly how much the Podcasts app said it was using. Had I actually been storing 12 copies of the same episode, it should have been much larger. (The numbers here are rough guesses, I don't remember what they were exactly at the time, but was exacting when checking, and the math did check out.)
I also checked the sum total size of the podcast audio files on of my laptop, and the Podcast App reported using pretty much exactly the same storage for all audio files as if I added up a single copy of all files that *should* be there for the podcasts I expected to be on the phone.
So while this seems like yet another screw-up behaviour of the Podcast App, at least in my case, it doesn't appear that it's something to worry a whole lot about, as the poodcasts aren't eating up space on your iPhone, at least if you're only seeing the duplicates while browsing the device in iTunes. Still another item on the list of reasons the default Podcast app needs to be fixed, though.
When I finally listened to the podcast in question, and it became marked for deletion (and at that point shows a "cloud" icon next to it, which I believe means the file itself is actually already gone from the device, and the "deleting" in 24 hours is just the item being removed from the list) the duplicates all disappeared from the iTunes view.