It sounds like Ty's guild has two types of players: Those who want to excel and rapidly move on to other content, and those who are happy to work their way through Kara at their own pace. Many guilds who aren't exclusively "hardcore" raiding guilds have to deal with this mix of personalities.
There are two ways you can handle this. First, you could put together a team of the most talented and motivated players your guild has. Find a night or two every week that works for all or most of those players. Then set out to learn, clear, and farm the entire instance. Once your "Dream Team" has mastered the instance and obtained the gear to make up for a few less talented players, they could open up the runs to others and help them to learn the encounters one step at a time. I firmly believe that most WoW players are eventually capable of handling any encounter they have the gear and consumables to manage, as long as they clearly understand what their job is during the fight. It just takes some people longer to learn the rhythm of the encounter and to avoid the costly errors that cause a wipe.
The key is to explain to your members exactly what the plan is for Kara. If you go for this first option, many of the players who aren't invited will become resentful unless they know that it will be their turn soon. If you're afraid some people still aren't going to like sitting on the sidelines, it may be necessary for you to set objective standards for this team. Set minimums like AP or spell damage for DPS classes, defense and stamina for tanks, etc. Don't create a Catch-22 by setting the minimums so unreasonably high that they can't be reached outside Kara. Also, make it clear that expensive enchants and consumables aren't optional for participation on this team. If a player thinks they have what it takes to contribute, they'll go out and get what they need -- and now by default they're more motivated than they were before. Hopefully that will carry over to their raid performance.
Some of your best players may not want to go back to Kara once they have everything they need. In this case, it's your job to remind them that moving on to Serpentshrine Cavern and beyond won't be possible unless they help to gear up more than just the original 10-man team.
If you have enough members to do so, your second option would be to form two teams: one team for your highly motivated individuals, and one for your more laid-back players. Typically those in the first category are harder on themselves and each other and can't stand to fail, whereas those in the latter group will tend to be more forgiving when people make mistakes. It's often this clash of perspectives that leads to arguments in raids. With this option, your motivated members won't be held back or frustrated by the others (at least in Kara). And those on the other team might find more motivation to play well if they aren't getting carried through encounters by better players.
Again, it's important to communicate how and why the teams have been chosen. Some of the players who aren't very good will still probably want to be on the highly motivated team. That's where your objective standards come in. At some point if one team is geared up as much as they can be, you might decide to mix the two teams together so that gear is put to good use and items aren't getting sharded left and right.
However, the bottom line is this: some people just aren't cut out for places like Kara. Overall, it's not an unreasonably difficult dungeon. However, encounters like Curator require a certain minimum overall dps, and Aran is notoriously unforgiving of carelessness. You might want to reevaluate in what direction you'd like the guild to be headed. Is it worth keeping players around that won't spend the time to learn how to optimize their class performance or prepare themselves properly for a raid, even after discussing it with the officers? Once you move beyond Kara, you're going to need 30-35 players you can count on. So if your plan is to progress beyond this 10-man raid, you need to either mold the players you have into solid raiders or find others who already are.
On the other hand, is it worth paying the price of progression if it means losing players that you enjoy having in the guild?
Ultimately, Karazhan is a place that forces you to decide what your guild is all about.
To my readers, how has your guild dealt with this instance? Are you raiding Karazhan, or is Karazhan raiding you?
Send Scott your guild-related questions, conundrums, ideas, and suggestions at firstname.lastname@example.org. You may find your question the subject of next week's Officers' Quarters!