This is a list of a few bugs related to cost reductions, certain zones and Inheritance. They may be related, so I'm presenting them here in one post:
1) Cards in a discard pile are (visually) not affected by cost reducers. See picture 1, with a Quarry and Villa in play, and a Villa on top of a discard pile. The Villa in play is correctly cost reduced to $2, the Villa on top of the discard pile still shows a cost of $4. The same effect happens with Highway, so this is probably not a specific card error. Also other zones are unaffected (tested trash, Native Village mat, Prince).
2) Cards in hand are visually affected by cost reducers, except inherited Estates. See picture 2, with a Quarry in play and a Ranger in hand reduced from $4 to $2, but the Estate-Courtyard still shown as costing $2 (it should be reduced to $0).
1) and 2) are visual problems, it is unclear if they extend to the actual game play. Mostly card costs matter for buying/gaining (so important for cards in the supply, not affected by Inheritance) and "trash for benefit" effects (Remodel,...), which means the trashed Estate is no longer inherited by the time the game is interested in its cost.
3) Chariot Race compares costs of cards not in play but under a player's control, so can be used to check if 1) and 2) are only visual problems. Unfortunately, at least for 2) the problem is real. In game #8539349 (Picture 3) on turn 13 Ingix plays 2 Charior Races, the last comparing costs of an Estate for each player. The game awared no VP in this case, which is generally correct but not in this case, as Ingix' Estate was just a Victory card 8still costing $2), while his opponent's was inherited and should have been cost reduced by the Quarry in play to $0.