Alts and Fairness
First off, the F-word: fair. As soon as you deviate from your usual raid-filled-with-raiding-mains bread and butter, things start getting a little grey. Fairness needs to be taken into consideration with many issues, from figuring out who can take an alt and who can't, to the distribution of loot and standards you hold players to.
The key principle I've learnt from experience here is to work things out in advance, lay them down on forums or elsewhere (raid chat, vent etc before the raid starts) and not to make things up as you go along. Of course, you'll run into new situations that demand an on-the-fly answers, but if you've got set rules and principles then you should be able to work these problems out easily. The majority of problems I've seen with fairness and alt runs were when people were winging it, and raid members started to complain because things started getting unfair.
What is fair? This might mean a different thing to your raid group than to others. For some, it's giving everyone an equal chance to take part. For others, it's working out what benefits the raid most. Perhaps it's rewarding those who put in more time and effort, either on mains or alts -- giving bonuses to the people who'll be there for the long haul. Or it's just for kicks and giggles, with the aim of having a good time (which includes pleasing as many people as possible with the loot decisions, too).
Putting alt raids together
When bringing in alts, there are really two different classes of raid. Firstly, a main raid that lets some people switch to alts, either because you need them for raid balance or because you can afford to have a few lesser-geared players along with a longer-term aim. An example here would be gearing up a shaman alt on Black Temple and Hyjal farm runs so that it's available to swap in for one or two Sunwell fights if needed. Since you outgear the content, having an undergeared healer won't really hurt the raid much, and the end benefit is more flexibility in your raid composition for Sunwell progress.
The second type of raid is a full alt run, with the expectation that most people will bring alts and standards set accordingly. You might not be breaking DPS records but everyone will get to have a bit of fun. An example of this is a BT guild putting together a Karazhan run on an offday. Most mains won't need anything from the instance (recipes or offspec gear, perhaps) and it's an opportunity for everyone to kick back and relax on different characters.
With either raid, you'll have composition requirements to fulfil, which is where the issue of fairness comes in. Is it fair that the same shaman alt gets to come on all Black Temple clears, when someone else's shaman lies gathering dust? The other players with shaman alts might say no, but the guild as a whole might say yes, as it enables one character to get Sunwell-ready rather than give assorted epics to multiple people with no benefit for the guild. In a case like this, you have to examine why you're letting alts into raids, and make sure that everyone understands it's not just so that particular person is rewarded with more purples.
When it comes to putting together raids comprised mostly of alts, composition becomes a major problem. Suddenly all your tanks are healers, all your healers are DPS and.. wait.. nobody has a tank alt? It's hardly fair that your MT has to tank on his nights off because nobody else could be bothered to roll a tank. Fortunately in my experience these things tend to even out, thanks to respecs and people realising the surefire route to getting raid spots on their alt. If you end up having to ask people to bring their mains, it really helps to keep track of who's had to play what, so that you can ensure it's not always the same person losing out.
Know your limits
Okay, so we're all superstar players with a superstar lineup of alt characters, all in full tier 6 and we can play all of them blindfold. Right?
There are three problems you can face when taking alts to raid content, even if it's Karazhan: gear, skill and preparation. Gear is obvious enough: a character that's newly level 70 in a handful of blues and levelling greens is hardly going to rock the Black Temple damage meters. This is more noticeable with tanks and healers, but even for DPS alts, things like having a large enough health pool can matter.
Generally, you'll set some standards for alts on raids to ensure that gear is at least sufficient for the content. Depending on how many mains you have along, and how draconian your guild usually is, you can choose to be fairly stringent or relax the rules. For example, you might want alts to meet Karazhan gear baselines that involve making some effort with crafted or heroic gear; Black Temple alts should have been to tier 5, and have a smattering of Zul'Aman and badge gear. Obviously everyone has to start somewhere, and making the rules too strict can just foster discontent, so you'll need to find a balance that suits your guild.
Skill is a debatable issue. If someone is fantastic at playing their main class, that doesn't always translate to their alts, which can cause some sticky situations -- having mediocre players doing stupid things because they're on an alt can make the runs painful for everyone involved. Sometimes you have to say no to people, although it's easier to do this in a positive light (we really need you on your main) than a negative one (you suck at your alt); note that they might find out the real reason eventually.
The advantage of being in a large raid guild is you're surrounded by good players of all classes and roles, so if someone's not very good at playing their alt, point them at someone who can play that class for some tips. Patience helps, too -- some abilities come faster with practice.
Finally, preparation. Again, the standards you set here might vary depending on your guild. A fairly serious endgame guild would probably require all alts to fully enchant their gear and put rare gems (ideally epics) in epic items, and bring full consumables to make up for any gear disparity. Others might make this more a personal choice, to make things fairer for those who don't have much time to farm. Barring someone from a run simply because their boots aren't enchanted can border on the petty, but seeing how people treat their alts' loot (and checking if they have the know-how to put the right gems and enchants in) is a really telling sign of how much they care about that character.
Drama-free loot distribution
On these alt raids, loot will drop. When loot drops, drama will happen -- you can almost guarantee it. This again comes back to the central concept of fairness, as drama usually arises because one person thinks they deserve an item more than another. Unless you're clear on the loot rules beforehand, you can almost guarantee you'll be accused of taking someone's side and giving them loot because you like them more.
A lot of alt raids and PuGs simply use rolling as a loot mechanic; this is fine, although it can lead to a fairly skewed distribution of items if one person simply gets lucky. If they do, fair enough -- random loot is random.
A general improvement to simply 'roll on everything' is to add a couple of caveats that tend to make the system a little fairer. Firstly, prioritise mainspecs -- a holy paladin rolling on DST
won't win it over that rogue. This gets a bit messy if someone's respecced so they could get in the raid, but assuming everyone knows their declared main spec (and they don't get huffy about not winning stuff for the spec they raided with) then you cut out most of the drama.
The second rule is one item per person until everyone has something. This can work out fair on paper but still lead to drama, of course, when people winning items early in an instance lose out on tier gear.
Alternative loot systems include loot council (if you particularly care about alts' enchants, for example, you can loot council items and penalise those without enchanted gear or those who underperform at their job) and good old DKP. DKPing alt runs creates a system that's roughly fair, and you can even award extra DKP to those taking mains, or allow people to use their main DKP to bid on rare items over alts.
What you do here obviously depends a lot on your existing loot system, but be careful; it's entirely possible for someone to stockpile a lot of DKP by taking a main and then bring in a freshly minted alt and loot everything
. Is this fair? On paper, yes, as they earned the gear -- but those competing for loot against them won't be so happy.
In general, allowing alts into raids is a positive move as it gives people a new angle to enjoy raiding from. However, beware of the pitfalls: raid spot drama, he's-in-greens drama, l2p drama and loot drama. By figuring out what's fair by your guild's standards, and what people are willing to sign up for, you can avoid a lot of this -- but beware of those who are simply loot hoovers without much of a clue, or your raids will end up full of them.