Article 7 of the FIDE Laws of Chess deals with Irregularities, and how they are to be handled. In my experience this is probably the biggest area of confusion for arbiters, although not so much for players.
There is one philosophical point worth pointing out here. One assumption made when drawing up these laws is that chess players do not intentionally cheat (even if they do from time to time). This means that we are not bogged down with pages of rules and regulations designed to restore 'equity'. Contrast this with the Laws of Bridge (for those that play both games) and you will see what I mean.
The first proposed change to Article 7 is to include a new 7.1, although this is essentially Article 6.13, now moved to a better location. The interesting thing in this clause is that it instructs the arbiter to also adjust the move-counter on a clock if needed. This explicitly allows the use of move-counters in FIDE rated chess events (although of course it does not mandate them).
7.2 Has a little bit of wording changed (to read better), but the intent remains the same. If the pieces are set up wrong at the start, the game is to be restarted, if the chessboard is the wrong way round, as per Article 2.1 (and not just because the numbers and letters are wrong), then the game is moved to a new, correctly orientated board.
There has been some extra wording attached to 7.5 (old 7.4) to cover some explicit illegal move cases. Leaving a pawn unpromoted on the back rank and capturing the opponents king are now specifically defined as illegal moves. To be honest I'm not fussed about this change, although it may help arbiters when dealing with argumentative players.
7.5b just adds the requirement that illegal moves must be completed (ie the clock is pressed), before valid claims by the opponent can be made.
7.6 deals with illegal positions/moves and how they are to be corrected. The need to conform with 4.3 and 4.6 has been added to this section, which means that if a position arises due to an illegal move, the replacement move must adhere to touch move etc (rather than playing any move that suits you).