In a blitz game, what is the ruling when both players make illegal moves, but the error is only called out after both moves have been played?
According to the FIDE Laws of Chess, illegal moves in rapid and blitz can only be flagged and punished before the next move by the opponent has been made. An illegal move which is identified late can only be corrected with the agreement of both players:
A.5.2 If the arbiter observes an action taken under Article 7.5.1, 7.5.2, 7.5.3 or 7.5.4 [i.e. an illegal move], he/she shall act according to Article 7.5.5, provided the opponent has not made his/her next move. If the arbiter does not intervene, the opponent is entitled to claim, provided the opponent has not made his/her next move. If the opponent does not claim and the arbiter does not intervene, the illegal move shall stand and the game shall continue. Once the opponent has made his/her next move, an illegal move cannot be corrected unless this is agreed by the players without intervention of the arbiter.
There is one situation where the arbiter can intervene after a series of illegal moves have been made and that is when an illegal position persists on the board for more than one move:
A.5.4 If the arbiter observes both kings are in check, or a pawn stands on the rank furthest from its starting position, he/she shall wait until the next move is completed. Then, if an illegal position is still on the board, he/she shall declare the game drawn.