Suppose the players misplace the position of King and Queen in a tournament game, what should the arbiter do according to the latest FIDE rules? Does the action depend on the time control/format of the tournament? Thanks!
The action taken depends on the time control.
For standard play (each player has 60 minutes or more for all the moves) the game is cancelled and a new game started.
For rapid and blitz (i.e. each player has less than 60 minutes for all the moves) the game is cancelled and a new game started only if fewer than 10 moves have been made. If 10 or more moves have been made then the game continues with the proviso that the side(s) with misplaced king may not castle.
Note that this will remain the case when the news FIDE Laws come in to effect in July 2017.
Some references from the current (2014 - 2017) FIDE Laws of Chess:
Glossary of terms in the Laws of Chess: standard play: G3. A game where each player’s thinking time is at least 60 minutes.
Article 7.2.a. If during a game it is found that the initial position of the pieces was incorrect, the game shall be cancelled and a new game shall be played.
Appendix A Rapidplay
A.1 A ‘Rapidplay’ game is one where either all the moves must be completed in a fixed time of more than 10 minutes but less than 60 minutes for each player; or the time allotted plus 60 times any increment is of more than 10 minutes, but less than 60 minutes for each player.
A.4 Otherwise [one arbiter supervising more than 3 games or arbiter not recording moves] the following apply:
a. From the initial position, once ten moves have been completed by each player,
(1) no change can be made to the clock setting, unless the schedule of the event would be adversely affected.
(2) no claim can be made regarding incorrect set‐up or orientation of the chessboard. In case of incorrect king placement, castling is not allowed. In case of incorrect rook placement, castling with this rook is not allowed.
Appendix B. Blitz
B.1 A ‘blitz’ game’ is one where all the moves must be completed in a fixed time of 10 minutes or less for each player; or the allotted time plus 60 times any increment is 10 minutes or less.
B.4 Otherwise [one arbiter supervising more than 1 game or arbiter not recording moves], play shall be governed by the Rapidplay Laws as in Article A.4.
According to the FIDE rules in the back of my USCF Official Rules of Chess 5th Edition, FIDE rule 7.1 states:
If during a game it is found that the initial position of the pieces was incorrect, the game shall be cancelled and a new game played.
This, however, might not be the "latest" FIDE rules. The book was copyright 2003.