World of Warcraft's Patch 3.3.2 added a random weekly quest to the Icecrown Citadel raid. The quest can be completed in both 10 or 25 person difficulty in the same week, and appears to be chosen randomly from a pool of five possible quests. The quests all begin from within the instance itself.

Blood Quickening - Blood Council & Queen Lana'thel

The raid must rescue Infiltrator Minchar before he is executed. This quest begins at an NPC directly to the left of the entrance to the Halls of Blood. The raid is given 20 minutes to rescue Minchar. The timer begins as soon as the raid sets foot in the Blood Wing, giving the raid 20 minutes to clear trash, kill the Blood Prince Council, and engage Blood Queen Lana'thel in combat. Once in combat it is alright if the timer expires so long as the raid is successful in defeating her.

Deprogramming - Lady Deathwhisper

This quest begins at an NPC outside Lady Deathwhisper's chamber. The raid is required to save Darnavan from Lady Deathwhisper's influence. Shortly after engaging the boss in combat Darnavan will enter the battle as a hostile NPC. He does significant damage and is immune to crowd control. The raid must off-tank him while killing Lady Deathwhisper. However, in order to complete the quest Darnavan must survive! It is important to avoid doing any damage to him, as his hitpoints are similar to a regular trash mob and he can be easily killed.

Securing the Ramparts - Rotting Frost Giant

If this is your weekly quest, it can be picked up from an NPC that appears from the elevator that you board after defeating Lady Deathwhisper. He will give you a quest that asks you to slay the Rotting Frost Giant. The Frost Giant can be found by clearing the ring around the outer spire, past the frost wyrm that guards the entrance to the Gunship Battle encounter.

This fight requires a little bit of strategy because the Rotting Frost Giant will periodically cast Death Plague, which will kill the player with the debuff if they are unable to spread it after 15 seconds. The simplest strategy seems to be dividing the raid into pairs of players, with each pair being at least 10 yards apart from the others. This is to allow the debuff to trigger while limiting the amount of damage it does to the raid. The Frost Giant will also cast a raid-wide knockback spell, requiring players to react quickly to reposition themselves.

Respite for a Tormented Soul - Sindragosa

This quest is given by Valithria Dreamwalker after her encounter is completed. Recipients of the quest are given an item called a Pulsing Live Crystal that must be used on Sindragosa when she is weakened. Upon using the item a 30 second channeling effect begins, after which the raid must defeat Sindragosa to recieve Crystalline Essence of Sindragosa

It is unknown whether every member of the raid must channel the item, or just one member. It seems likely that only one member would be required to channel it given the mechanics of this fight, and the fact that it seems to be intended for use in Phase 3 where staying in line of sight for 30 seconds, let alone channeling a spell, can be a death sentence. This seems to be the hardest of the weekly quests by far.

Residue Rendezvous - Festergut & Rotface

This weekly quest requires the raid to return to Alchemist Adrianna while infected with Orange and Green blight. The orange blight is obtained from Festergut, it is the ambient gas cloud that infects his room during the encounter, meaning that as long as anyone survives the fight they will have the Orange blight. Rotface gives the Green blight; this is obtained by allowing yourself to be hit by his slime spray. You need only be hit by it once, players are not required to sit in it for the full duration.

This quest can be tricky, because the debuffs are removed upon death and have a 30 minute duration. Divine intervention and divine shield also remove the debuff. This means that the raid must kill the bosses back to back without wipes. Luckily, only one raid member is required to have the debuff for everyone to get credit for the quest! There have also been instances where raids have wiped, but a hunter has managed to feign death with both debuffs and save their raid from failing the weekly quest.

Quest Rewards

Upon completion of any of the weekly, players will recieve a Sack of Frosty Treasures and a gold reward. The sack contains a gold reward that seems to range from 9-35g, and 5 Emblems of Frost. There is also a low chance for the sack to contain an ilvl264 bind on equip epic item. It seems as though any bind on equip that is obtainable in the instance can drop from the sack, not just epics that drop from trash!