This is mainly for my own sanity, but also for others', so that there is a single place I can always refer back to for this. I will add more as I or others think of them.
Possession/OutpostThe rulebook for Alchemy does a pretty good job of explaining a lot of the nuances of Possession, and devotes a lot of space to Outpost in particular. Both of these cards cause an "extra turn" to be played - the former by the player to your left, and the latter by you.
We learn that if Adolf plays both a Possession and an Outpost on his turn, the Outpost resolves first, since it is Adolf's extra turn, and then Possession is resolved, since it is an extra turn with Eva's hand.
We also learn that if Adolf tells Eva to play Outpost during the turn where she's being Possessed, she then takes her Outpost turn after the Possessed turn, then proceeds to take a normal turn - 3 turns in total, the first being controlled by Adolf, and the second starting with a 3 card hand.
What the rulebook does NOT address is what to do when Adolf plays TWO Possessions, and makes Eva play an Outpost during the first Possessed turn. The key to figuring out what to do is that both cards produce an "extra turn." Now, Outpost does two things - it causes something to happen at Clean-up (only draw 3 cards), and it creates the extra turn. This is important. So let's take this step by step.
-Adolf plays Throne Room on a Possession.
-Adolf takes his first Possessed turn of Eva, making her play an Outpost.
-Outpost causes Eva to draw 3 cards at Clean-up instead of 5.
-Two things are trying to happen at once: the extra turn from the Outpost, and the extra turn from the second Possession play. Since Adolf is controlling Eva during Clean-up, he gets to make the decision:
----If he chooses to play the Outpost turn, Eva retakes control for a 3 card hand. She then draws 5 cards, Adolf takes control again for the second Possessed turn, and then Eva finally gets to take her normal turn.
----If he chooses to play the Possessed turn, Adolf controls Eva for the 3 card hand, and the extra turn generated by Outpost fails to happen, since Outpost can't produce a third (or more) consecutive turn. So after the 3 card hand, Eva takes her normal turn.
This logic follows no matter how many Possessions Adolf played, as long as he makes Eva play Outpost with at least one more Possessed turn left to resolve, except that if the Outpost is played in any turn other than the first Possessed one, there will be no option to take an Outpost turn - Adolf will retain control of a 3 card Possessed hand.
Ironworks/TraderAlso known as the Blue Dog rule.
This combination took a lot of arguing and a lot of dithering back and forth on what actually happens. It mainly came down to Ironwork's ambiguous wording. "Gain a card. If it is a..." This wording does not stipulate whether "it" is the card selected, or the card actually gained. Eventually Donald X. decided that "it" refers to both - the bonus only happens if the gained card is the selected card. And the reason why this matters is because Trader (almost) uniquely says "When you WOULD gain a card..."
Take Ironworks step by step. First gain a card. Then do something because of the card you just gained. When you reveal Trader, Ironworks is no longer gaining a card, so that first step no longer happens. Therefore the second step cannot happen either. Think of "If it is..." as shorthand for "If you did, then if it is..." So if you Ironworks a Great Hall, and reveal Trader to gain a Silver instead, you do not get +1 Card, +1 Action. You get nothing.
Similarly, Possession refers to "would gain" - if Adolf makes Eva Ironworks a Great Hall on her Possessed turn, Adolf gets the Great Hall, but Eva does not get +1 Card, +1 Action, much to Adolf's chagrin.
Hermit/SchemeThis is one odd example where the rulebook actually gets it wrong. I quote:
"If Hermit is not discarded from play during Clean-Up, for example, if you put it on your deck with Scheme (from Hinterlands) - then the ability that trashes it will not trigger."
The ruling is correct, the example is not. This is because Scheme does not prevent a card from being discarded - it just does something to the card after discarding. Scheme very clearly states the card has to be discarded, which is why you can't Scheme Duration cards played that turn. Scheme says "If you discard..." and not "If you would discard...", so there is no ambiguity here.
So when you discard a Hermit during Clean-up having played Scheme and having not bought anything, two things try to happen at once. 1) Trashing the Hermit and gaining a Madman, and 2) Putting Hermit back on top of your deck. If you elect to perform 1 first, then Hermit goes off to the trash, and when 2 comes around, Scheme has lost track of it and can't put it back on top of your deck. If you elect to perform 2 first, then Hermit goes on top of your deck, and then Hermit loses track of itself, and fails to trash itself. However, the gaining of Madman is not contingent on the trashing of Hermit - it is only contingent on the not buying anything. So even though Hermit was not trashed, you still gain a Madman.
This ruling was actually given during the Dark Ages previews before the rulebook was even officially published.
Throne Room etc./Any DurationAs stipulated in the rules, a Throne Room played on a Duration card remains out with that Duration card until your next turn.
What is not stipulated in the rules is what to do with a Throne Room played on that Throne Room. According to Donald X, that first Throne Room is discarded during Clean-up, since it is played on a non-Duration card.
However, when Throne Room is played on a Tactician, it is not left out, as the effect of Tactician cannot be doubled. Throne Room only stays in play on a Duration if it actually effected a second play of the card.
This applies to King's Court, Procession, and Band of Misfits.