I feel the OP's pain. Something has changed in iTunes since Mavericks. Used to be if you subscribed to a podcast through iTunes, it synced down to the iPhone/iPod just fine, no problems. You could play them through the Music player just fine. But now, since the advent of the Podcast app, for some unknown reason, every so often a podcast downloaded through iTunes will show a cloud symbol to the right of the name in iTunes, indicating that it isn't downloaded (even if it is) and sometimes the length of the podcast is shown as "Continuous" even when it isn't. And when you download through iTunes and sync, then open Podcast, the podcast isn't there and has to be directly downloaded in Podcast. So, as the OP said, you end up downloading twice. I have searched all over for a solution, but came up empty. I want the podcasts on my MBP and on my iPhone, so I just go ahead and download twice. PITA, but it's what I have to do. I don't know if it's iTunes that is broken or IOS7, or Podcasts, or what, but the sync function that used to work just fine is now broken badly for podcasts.
EDIT: Strangely, there is a very similar problem I am having with iBooks and ebooks as well. They don't sync, with iTunes saying it cannot find the file, but the files are there on the MBP, iBooks can find them and the files are on the iPhone, and iBooks there can find them. They just won't sync. So I think the sync function has been messed with and is now unreliable as it was.