I've just replied to an old post started by Michael back in July 2014 regarding the 1 minute remaining issue.
https://discussions.apple.com/thread/6452750
Have had this on and off for as long as I can remember, but over last 12 months all seemed fine - now it's back (though only when playing Podcasts via iDevices). Any Podcast played via the iMac work as expected i.e. when finished they are marked as played, moved below "Episodes to be Deleted" and are removed after a short while.
Can't work out if it's the fault of the iPhone/iPad either in the Podcast app itself or some screw up from using old restore backups - or Apples Network getting it's
knickers in a twist and failing to recognise played positions properly, especially towards the end (but that doesn't explain why the iMac works unless they use different Network Centres!).
If I play a Podcast on either iDevice or iMac and stop part way through the others do pickup at the correct point to continue (so play position sync seems to be working ok) but the iDevices just fail to hold on to that last minute, and the played Episode reappears with 1 minute remaining after a short time (but only on the iDevices - on iMac they remain marked as fully played). If played to the end via the iMac they all seem to remember and they remain as played.
There must be a way to Reset Podcasts so you can start afresh, but unsubscribing, deleting or unchecking the sync box on the iMac seems not to work because on resubscribing previous play info also reappears and you are back to square one again (is this info coming from Apple or is it retained on our
iDevices/iMac in some file?).
Someone must know more on how Podcast syncing works (and communicates with Apples Network) that can shed some well needed light on this frustrating glitch......anyone!