At this point I consider myself a Karazhan veteran. I've seen the place repeatedly from three different perspectives: tank, hunter, and shadow priest. I really like it -- the fun part is that the bosses present a variety of challenges. Each fight places the focus on a different sector of your group, and I like the flow and feel of the bosses fitting together. Here's a quick walkthrough of the bosses for posterity, in the usual order that a very well-geared group will do them:
Attumen: This is a tank gear check, plain and simple. Midnight and Attumen are both tank and spank; if your tanks can take damage, you win, otherwise, you lose. A good warmup.
Moroes: This fight is about crowd control. Basically, if you keep a couple of guys under control, it lets the healers rein in their aggro, and makes the fight much much easier. If shackles or traps break or are fumbled, you're in big trouble, with many adds capable of rampaging. A coordination check on the raid.
Maiden: This fight is about dispelling reflexes. The only real obstacle to this fight is Maiden's holy fire, a nasty DoT which needs to be cleansed quickly. A good trigger finger on the dispel squad and you should be okay. (It helps to have a clueful paladin keep up blessing of sacrifice, of course.)
Opera: Three different possibilities:
The Wizard of Oz: This fight is really about the tanks. Fearing Roar is not hard; kiting the strawman with fire is not hard. But one tank needs to kite the tinman around, and he hits hard; the other tank needs to tank Tito and maintain secondary threat on Roar. Well, not needs, but attentive tanks who pick up the adds when they spawn will make this fight a win for you.
The Big Bad Wolf: This fight is about the healers being ready to spam heals on Little Red Riding Gnome. Secondarily, it is an individual responsibility fight, as people have to be ready to run.
Romeo and Juliet: This is one for the spell interrupters; the fight is more or less trivial as long as Juliet's heals are interrupted.
Nightbane: Another (optional) tank gear check, with some personal responsibility mixed in. The tank also needs to be good about positioning and churning out threat quickly on his relanding, because he can and will 1-shot dps serially until you do.
Curator: This fight is about dps, who need to switch to the flares quickly and eliminate them before they drain the healers' mana pools. Secondarily, it is about the healers cleaning up after the chain lightning. Incidentally, this is the easiest fight in Kara to tank; because the DPS are mostly after the sparks, you basically have to do nothing more than keep your uncrushability up. Yawn.
Illhoof: This fight is about dps, similar to Curator: nuking the demon chains super fast = win. This is harder than Curator, because the sacrifice is more urgent and less frequent than the sparks, so it's more about reflexes and less about intelligence.
Shade of Aran: In my opinion, this is the hardest fight in Kara from a coordination standpoint, dealing with the elementals, who always cause chaos and interact poorly with each of Aran's special abilities. This means that the main people under duress will be the healers, who have to be prepared for bursty damage on anyone and complete chaos during the elemental phase. Secondarily, spell interrupters need to do their job.
Netherspite: This is an incredibly well-rounded fight. You need teamwork, gear, and individual smarts to prevail. The most fun fight in the instance, bar none.
Chess: This fight is about relaxing and picking up two easy badges.
Prince: Despite the fact that this is the last fight in Kara, it's mostly a luck fight. If the infernals don't drop between Prince and the door, this fight is really, really easy. If they do, you're in for a world of unavoidable pain (especially if you have lots of melee.) This is a really easy fight to heal; either people die after enfeebling, or they don't. It requires some gear, but less than either Netherspite or Nightbane; I would say that it's much more straightforward than any fight in Kara with the exception of Attumen.
Anyway, it's a fun ride, one which I look forward to doing many more times.