One of the biggest factors in WoW is responsiveness. No matter how much you plan and prepare for pulls or boss encounters, there's always some level of uncertainty influencing the game. Latency spikes aside, there's always the chance of an unlucky string of attacks, or of an additional pull that you couldn't see joining in the fray, or of a glitched frost block.
One example: I've run through the Culling of Stratholme many, many times, but I'll always remember the run in which Mal'Ganis improperly reset, subsequently becoming an unkillable beast that locked in endless combat with Arthas. My party watched the two combatants duke it out at 1 Health each for about 10 minutes, and then shrugged and walked out - we didn't really need the spare emblem, anyways.
On a more practical note, I always stress the importance of raid awareness to my groups on runs. This goes for simple things, like not standing in the charred earth, or getting out of void zones. It should also hold for more complex behaviors: if adds spawn and attack you, move to a tank to have it picked up; when fighting a boss with AoEs, ranged DPS should use a rangefinder to make sure that they're minimizing their exposure to that damage. In general, I see pretty good responses to these things.
Raid responsiveness, meanwhile, is where I'll be turning my attention. This is particularly applicable to tanks, and I know that I've practiced responsiveness heavily. Any option slots that can improve my mobility have been put to use for just this purpose - I'm not concerned with my survivability or threat generation in current content, but I can always improve on snapping to my healers to pull back a rogue add in an encounter.
But what, then, is the difference between awareness and responsiveness? Part of it lies in the activity of the verbs: To be aware of something is good, but to respond correctly to that which you've noticed is even better. More importantly, I'm thinking of responsiveness as applying to things which the raid leader may forget to mention, or which may not be scripted into the encounter.
For example: If you jump in to Noth without making a note of the imperative decurse requirement, how likely are the mages to notice curses landing on party members, and how will they respond? Or, if you engage Heigan as a Fury-Specced warrior and watch the MT and OT go down to latency during the dance, do you have your shield ready to swap-in so you can pick up tanking? Or, if you're in P3 of Malygos and you happen to slip away from the pack, do you know how to build a self-healing cover into your DPS rotation until you can find your way back to the team (or pop your speed booster to get back to them faster, without letting your Engulf in Flames stack drop)?
These "good habits" and natural responses do not come naturally to most players. Even raid-seasoned DPS will likely ignore the need to remove debuffs from allies in favor of shoving their own Recount meter just a little higher. For old content, this is probably a fine thing - your healers are likely looking for something to heal, anyways - but that should be the exception to the rule, rather than treating progression as the exception to all other runs.
I guess a lot of this boils down to a shift in priorities. Simply dealing damage or building threat on the main target is not always the top priorities of raid players; knowing when to switch - and how to switch efficiently - will make your runs smoother, even if they happen to take a little longer than you'd imagine. Chances are you'll actually save time, because saving the life of a 1.5k DPS player is far more valuable than ignoring him to get another 50 DPS on your meter on a boss encounter.
Whose responsibility is it, then, to be responsive? Do the Tanks and Healers alone cover these needs, while the DPS should just run their rotations? If that's the case, do we actively expect better players to take up the roles of Tanks and Healers? How do we then scale the requisites for taking on such classes? "If you want to tank or heal, prove that you can; if you want to DPS, welcome aboard"? In the end, is responsiveness really that taxing of a practice to employ in any class's playbook?