One way to prevent the "rats" from taking over games and not being punished for dirty play is to get rid of or change the instigator and third man in rules.
During the playoffs last year, New York Rangers forward Brandon Dubinsky jumped into a fight between teammate Brian Boyle and Ottawa Senators defenseman Matt Carkner. Carkner began attacking Boyle, even though Boyle wasn't fighting back.
Dubinsky was ejected for being the "third man in" during the fight, even though he was trying to help his teammate who was attacked in a cheap manner. Dubinsky was rightfully upset, and the whole incident gave people a stronger argument for getting rid of the third man in rule.
Taking away the "Third Man In" and "Instigator" rules would make players be accountable for their actions. If dirty players had to be more accountable for their play, we would see less injuries.
According to the NHL rulebook, here are the descriptions of the two rules.
46.11 Instigator—An instigator of an altercation shall be a player who by his actions or demeanor demonstrates any/some of the following criteria: distance traveled; gloves off first; first punch thrown; menacing attitude or posture; verbal instigation or threats; conduct in retaliation to a prior game (or season) incident; obvious retribution for a previous incident in the game or season.
A player who is deemed to be the instigator of an altercation shall be assessed an instigating minor penalty, a major penalty for fighting and a ten-minute misconduct.
46.16 Third Man In—A game misconduct penalty, at the discretion of the Referee, shall be imposed on any player who is the first to intervene (third man in) in an altercation already in progress except when a match penalty is being imposed in the original altercation. This penalty is in addition to any other penalties incurred in the same incident.
This rule also applies to subsequent players who elect to intervene in the same or other altercations during the same stoppage of play.
Generally, this rule is applied when a fight occurs.
If you eliminate or change these rules, the players will police themselves better and the amount of dirty hits could certainly decrease.