Basically Inheritance turns your Estate into a $2 Estate that gains the abilities and types of the card you set aside. It doesn't work with Crossroads because you still played an Estate, not a Crossroads, as mentioned above. Few other examples/interactions relating to other cards, some have which been discussed above (correct me if I am wrong):
Swindler: If the Inherited card gets Swindled, it gets turned into another $2 card, either Estate (which still becomes Inherited card) or other $2.
Treasure Map: Doesn't work, your Estate is not a "copy of Treasure Map" as Donald already mentioned.
Potion-cost cards: Can't use it on these, just like you can't use Workshop or Ironworks to gain them.
Baron: Mentioned above, Still works, since you are still discarding an Estate.
Young Witch: Can't reveal the Estate as a Bane, as the Bane card is never an Estate.
Squire: Does work, you can trash your Inherited Squires to become attack cards, as card text says "when you trash this".
Sage: does not combo with Inherited cards, since the Estate still costs $2, and will pass over them.