We don't stop playing because we grow old; we grow old because we stop playing.
What is the correct procedure if a player plays enough cards to finish a building for which there is not enough empty space on the board, that is, one that can't be built?
The rules state that the cards are discarded. My question is, what cards? Only these last played by the finishing player, or all of those exposed before by this or other players too?
All cards of that type on the table (all players) should be discarded. You can confirm it playing the game on BSW.