Last night we did Nightbane with:

Feral Druid (MT)
DPS Warrior (OT)
Rogue
Resto Druid
Mage
Resto Shaman
Shadow Priest
Warlock
Paladin
Holy Priest (Horde; no fear ward)

It went surprisingly well!

That is the most colorful post I've ever seen.

As for our group, we run too melee heavy. We have been using 2 Feral Druids, 2 Holy Priest, 1 Prot/Fury Warr, 2 Enh Shaman, 1 Rogue, 1 Mage, +1 (usually mage or hunter). Illhoof was essentially impossible for our makeup/gear level. We could get Aran down to the low 20s high teens percentwise, but we had no good way to deal with the elementals.

To switch it up, I'm (Feral Druid, Tank 2) am going to go healing, and one priest is going to go shadow. That +1 is likely to become a warlock. Although we don't expect the bosses to simply fall over with the rearrangement of talents + addition of a warlock, I foresee both Illhoof and Aran dying on our next reset.

I highly recommend adding a warlock to your group. My groups first clear of karazhan (except nightbane and spite) was without a warlock, and Aran was hands down the hardest boss for us (Prince took longer but only because of his bugs). For our second week, we swapped a warlock for Aran and it became a much simpler fight. The updates to Illhoof also make a warlock very useful. We originally killed his easy version with one AOEr (mage), but after his buff, one mage couldn't handle it by himself anymore; his mana was gone long before Illhoof was.

Needlessly complicated. Most of the things you "need" you'll have with a balanced group. There are only a couple of specific fights where certain groups will have a much easier time.

Attumen: 1 tank, 1 OT. Healers and DPS.
Moroes: 1 tank, 1 OT. Healers and DPS (2 priests).
Maiden of Virtue: 1 tank. Healers and DPS.
Opera - Romulo & Julianne: 1 tank, 1 OT. Some interrupts, purge/spellsteal. Healers and DPS.
The Curator: 1 tank. Decent burst DPS. Healers.
Terestian Illhoof: 1 tank, 1 OT. AoE, burst DPS and healers.
Shade of Aran: Interrupts. Warlock. Healers and DPS.
Netherspite: (still havn't done! )
Prince Malchezaar: 1 tank. Healers and DPS.
Nightbane: 1 tank. 1 holy pally. Healers and DPS.

What group will have what is needed for every single boss?

1 Prot Warrior - Main Tank
1 Feral Druid - OT or DPS
1 Shadow Priest - DPS
1 Warlock - DPS
1 Mage - DPS
1 Rogue - DPS
1 Holy Pally - Healing
1 Holy Priest - Healing
1 Shaman - Healing
1 Hunter - DPS

I cant think of a group I'd rather have if there was a race to clear the instance from beginning to end. It can do every encounter very well.

I'm biased but...

Replace the Holy Priest with a 2nd paladin for an extra blessing for everyone in the raid and an extra aura. Put the 2 paladins in the shadow priest's group and they will never ever ever run out of mana ever (spiritual attunement is hax). One of the paladins can also act as the 3rd OT as/when needed.

Currently, my guild has found that any group can basically clear up to and through Curator. Past Curator melee DPS becomes important for the trash pulls and the kick/pummel/shield bash on Shade. Prince seems to require at least 3 solid healers and a Shadow Priest, with ranged DPS being important to avoid the AoE attacks from both the boss and Infernals.

Our Team 1 normally use the following:

Warrior (MT)
Warrior (OT)
Holy Priest
Holy Priest
Tree Druid
Shadow Priest
Mage (Frost or Fire)
Warlock
Warlock
Rogue

However, we have subbed out on various occasions a Holy Pally for a Holy Priest, a Hunter for a Warlock, and a Ret Pally for a Rogue (not much to my liking, but eh...).

Team 2 is just starting and they are using:

Warrior (MT)
Warrior (OT)
Holy Priest
Holy Priest
Holy Pally
Mage (Frost)
Mage (Fire)
Warlock
Warlock
Rogue

This combination did NOT seem to work for them. Partially due to their lack of gear and partially because of the lack of a Shadow Priest. I cannot stress enough how important a Shadow Priest is on almost all the encounters. For the early encounters they are not as important but come the Curator and beyond they are extremely vital.

Now, one question I do have, has anyone encountered problems with some of their members complaining about off-specs being allowed (or not) into their raids?

Traditionally, Shadow Priests were considered an off-spec but, since TBC, have become critically important. Likewise, Feral Tanks have really come into their own. I have continually been running into a problem with Ret Pallys though, since they see Shadow Priests and Feral Druids in raids and can't understand why they aren't in the raid as well.

Has anyone found a really viable use for a Ret Pally or even a Moonkin Druid that cannot be fulfilled by another, better suited class? At least in Karazhan I have yet to find an encounter that either of these spec lines would shine in.

Furthermore, without the gear to support these specs is there any reason to take these off-spec classes?

EDIT:

We have a Shammy coming up in the ranks soon and having never played horde-side I was wondering what the best function he might serve as well? Healer, DPS, both? Who could/should that person replace with the teams I have listed above?

Yes, there is. See the Nightbane thread.

A second pally over the Holy Priest would work well too. I think I just prefer the priest so you have a little more variety in the healers (Mending, yadda). The second shackle is also nifty for some bits and trash.

Sure, there are specific places where these would be useful (though not necessary), the problem is that they are not useful in all places, and with 10 men you can't afford to have someone being not useful at at time unless you want to make it hard for yourself.

Blessings make a pretty big difference.

Blessing of Kings (Tank)
Blessing of Might (Melee dps + hunters)
Blessing of Wisdom (Casters)
Blessing of Salvation (Warlocks, Shadow Priests?).

Out of interest does the ret paladin have a ctprofile?

I'd personally be willing to give a decent moonkin a shot in a 25 man raid once we get there. Not a spec that personally grabs me but the combination of a 3% +hit bonus to physical damage dealers raid wide and the 5% crit aura to party spell casters is a pretty solid contribution. Couple that with another innervate and battle res and provided said druid can do a respectable amount of dps/shifts to healing when needed I'd consider it worth the trade off of one pure dps class.

Wouldn't favour one in a 10 man raid, same arguement as with ret paladins plus not going to get a full spellcasting party going as easily and definitely don't need two for a 25 man since not getting the benefit of improved Fairie Fire twice. Other issue is that with no threat control and a fairly high crit approach they're going to need to have decent judgement about their agro at times. All a bit of a non issue for us at the moment admittedly since our raiding druids are resto or feral.

Aggro is really no problem when you have pallies and decent tanks.