Rule 13.7a states that spectators are not allowed to speak about or otherwise interfere in a game. Common instances of this rule being broken are when an illegal move is made or when a player's flag falls and a 'spectator' points it out, gestures, or simply gasps, thereby drawing attention to the fact. If this occurs, usually in a time scramble, it's unfortunate for the player whose flag has fallen, because his opponent may also be very short of time and had not noticed the flag-fall. But the result of the game stands. There's no requirement or option to replay the game (NB. it is an option under US Chess Federation rules, which differ from FIDE's), or for the game not to count for grading or rating purposes. It's important that young players are aware of this rule as they are often the culprits.
In the event of a spectator offending this rule, the arbiter may expel that person from the playing venue. In most cases, however, the spectator would just receive a warning.
Spectators are allowed to inform the arbiter (but only the arbiter) if they happen to observe an irregularity.
No one (including a 'spectator') may use a mobile phone or any kind of communication device in the playing area and any contiguous area designated by the arbiter (Rule 13.7b).
Finally, the following 'rules' have been extracted from a US chess site. They are intended to apply equally to spectators and parents, as well as to players observing other players' games. They are all perfectly valid in this country (except we call them 'crisps' - see #8):
1. Don't 'camp out' to watch a particular game.
2. Don't stand in front of or make eye contact with any player whose game you are observing.
3. Don't make faces or gestures or convey in any graphic way an opinion of the game being observed.
4. Don't discuss or even whisper an opinion of a game being observed.
5. Don't speak privately with any player at or away from the board while his or her game is in progress.
6. Don't take pictures after the first ten minutes of a game when using flash or a camera with an audible shutter unless you have prior approval from a tournament official.
7. Don't take pictures at any time from a location that makes you an obvious distraction to the players.
8. Don't make any noise, such as opening a bag of potato chips, within earshot of a game in progress.
9. Absolutely do not point out flag fall or illegal moves, or otherwise attempt to play the role of tournament director by intervening in a game for any reason.
10. Don't discuss a game at its conclusion in the tournament room or attempt to analyze a game at the board.
11. You may make a tournament director aware of concerns about perceived cheating or rules violations of players or other spectators, but do not attempt to enforce rules yourself.
12. Do, of course, comply with any requests or instructions issued by tournament staff. Be aware that a tournament director may ban spectators from the viewing area if necessary.