Don't poke the beehive
First and foremost, you must never do anything to further antagonize any situation that looks as thought it might get out of hand. If a player expresses concerns about loot or another raid member, you should immediately intervene to prevent any form of public disruption. Take the matter to whispers, to a private channel, or to a separate Vent channel. Allowing any issues to persist in the general chat only invites more people to become involved, which can quickly lead to things spiraling beyond anyone single person's ability to control.
Despite what it might seem, it isn't a matter of attempting to admonish players in private or to gang up on anyone; it is merely a matter that some things are not the business of others. If a player has an issue with another raider or with the way a particular piece of loot was handled, then that is a matter which should be discussed only between the parties involved. No one else needs to add in their two cents. Doing so only creates confusion, discord, and discomfort among the ranks. Personal matters are personal; they don't need to involve everyone and their mother. Keep them out of the public sphere.
One thing you must absolutely avoid is causing a scene of any kind. Politely ask the party or parties involved to join you in a private discussion, and leave it at that. Do not take any more action than that. If a player refuses to due this, then take more appropriate measures to keep order. If it's a raid matter, then remove the player from the raid. This isn't a permanent thing, just a measure to keep them from stir up additional trouble inside of the raid chat in general. If you also happen to share a common guild and it spills over to there, then demote the player to a rank that doesn't have guild chat access.
Again, you aren't seeking to outright punish the player, and that needs to be made clear. You are, however, attempting to remove distractions from the core issue -- fixing the problem that has occurred. Should a player not wish to behave themselves to allow for this, then you merely must do what you must to keep order, nothing more and nothing less than that.
Remain entirely neutral
Another imperative when dealing with any player disputes that you absolutely cannot take sides. This is especially important should the issue be between two players themselves, but even in matters of loot, you cannot initially defend any one party. Once a problem occurs, the first order of business is to make sure that you get the facts of both sides of any story directly from the players involved. You may already be aware of how something started, but your perceptions are entirely relevant to the matter at hand. What matters more is how the players involved see things.
Often, issues arise because of simple misunderstandings or someone's taking what might have been meant to be a joke personally. In these instances, whether the joke was merely tactless or the offended party is taking things far more to heart than need be, the truth isn't really all that important. What all of those involved think, feel, or believe will hold more weight than anything else. When it comes to player disputes, truth is a relative term. You must understand that any attempt to make people see "truth" or "what really happened" is, in reality, your attempt to impose your perceptions on them -- something people normally don't take kindly to.
While there might be a "right" or "wrong" side of everything, the simple fact is that perception is everything. Challenging another person's perceptions on the matter is going to lead to nothing more but an all-out confrontation. Instead, listen to all sides, take into account every part of the matter, and the discuss in neutral terms how the issue can be solved. One thing to keep in mind on matters of loot is that while you do have to listen to all sides, you must remain unwavering in defending how it was handled, especially if you operate on a loot council system.
Players may disagree with the way that loot was handed out, but they cannot change what has been done. Unless the player in question's concerns are entirely legitimate, in which case you need to seriously reevaluate your loot system or have a strong talk with your council. Allowing a loot reversal because of player complaints opens up a bad door that you do not want to step through.
While many situations end once a dispute has been handled, we only wish that we could be so lucky. If you have two players that have a falling out that ends with one of them exiting your raiding team, you must make it clear in no uncertain terms that the matter is settled, cleared, and done. There is no point in bringing it up once again. Disparaging remarks from anyone about either side of event cannot be allowed to play out inside of a raid. A player may no longer be a member of your raid, but that doesn't usually change how players feel about that person. Even if you have one or a large group of fellow raiders that didn't care for nor get along with a prior member, that doesn't mean that everyone shares the same sentiments.
If you allow players to continuously bring up old wounds, then you can never really move on from them. The matter will never truly be resolved because no one will forget it. Further, there may still be players in your raid who are friendly toward your ex-member. Allowing your raiders to have a whispering campaign against another player is only going to lead to ever-larger problems. All it takes if for one person to rely these comments back to the other player, and soon you can end up with a conflict that spans the server itself, spilling out into trade and general chats in ways you don't even want to imagine.
Remaining personally aloof
In a similar vein, you must absolutely, under no circumstances, make any snide or undignified remarks of your own against another player. Not to sound entirely paranoid, but you never really know another player's stance on certain issues. They might say certain things so as to go along with the crowd but in truth, they're repulsed by what you say or relying every word to the person in question. You could not even begin to guess the number of times that I've heard of people screenshotting or forwarding whispers or presumably private conversations from one group of players and showing them off to others.
Raiding groups and guilds, just as every other social group, have a tendency toward gossip. Gossip is a naturally self-destructive state. You don't have to admonish every ounce of nay-saying from your raid member, nor do you have to scour the ranks to make sure that everyone upholds an idealistic code. But you shouldn't let things get out of hand nor go too far; further, you should refrain from participating yourself. It goes against basic nature, I'm sure, but taking the high road certainly is the best option.
Clear, open communication
Last, it's good to remember that nothing is a better method of dealing with these types of issues than preemptively ensuring that they never come to pass. Look for all of the signs that players may have a growing distaste for each other and see what it is that you can do to alleviate some of their stress. Generally, players aren't that hostile toward one another -- it's usually minor, small issues that really shouldn't be worth noting -- but they build up over time until eventually everything just spills over.
Further, be on the lookout for anything that might cause loot issues. If there seems to be a slight, growing discontent over the way that loot is handled within your raiding group, then start opening the floor to hear suggestions on how it might be better handled. While things might not change, often the best way to convert people to your way of thinking is to allow them the sense that they have a personal stake in the matter. If players believe that they are contributing, then they are often more at ease with any system you have in place, regardless of whether anything actually changes or not.
Finally, open communication is often the best policy in any raiding group. Having an open forum or place where players can discuss any matters that they might have with the raid or how things are handled goes a long way in ensuring that everyone remains happy. Along with a public line of communication, always be open to private talks with players over any matters that they might be having problems with, be it other players or otherwise. Some things are best not said in public, particularly if they are of a personal nature, but they too need to be talked about if conflict is to be avoided. The success of any good raiding team is communication.
Ready Check shares all the strategies and inside information you need to take your raiding to the next level. Be sure to look up our strategy guides to Cataclysm's 5-man instances, and for more healer-centric advice, visit Raid Rx.