Over in the strategy forum someone discovered that when calling Coin of the Realm (because of Caravan Guard) on another player's turn, the CotR stays in play until your next Clean-up. This matters rarely for CotR (because you generally wouldn't call it in another player's turn), but matters for Duplicate. And actually the Adventures rules specify that Duplicate is discarded in the current player's Clean-up. This is wrong online.
Just as an aside, the old Outpost also would sometimes be discarded in another player's Clean-up.
The implication is clearly that all players' cards in play are discarded in Clean-up, not just your own cards. (Durations of course following their normal rule of not being discarded if they're not done).
I guess that for current cards this only matters for Coin of the Ream, Duplicate and Royal Carriage. I don't think there's any other way for a card to end up in your play area when it's not your turn. If there was a way a Duration could be done with its future effects on another player's turn, that would also invoke this rule, but I don't think there is. Still, strictly speaking, this should be a fixed as a general rule.