Let's break up the basics for ease of discussion.
Situational awareness and positioning
The days of lining up on a boss' behind and thwacking away with impunity are long gone in most cases. Bosses have cast time abilities (some which can be interrupted, some which can't), various don't-stand-in-me effects occur, some situations call for getting out of line of sight. A warrior who refuses to do anything but pay attention to his or her rotation is most likely a dead warrior.
Frankly, this is what the heroics are designed to teach you to do, and if you haven't been paying attention and have been wiping a lot due to an inability to wrap your head around this idea, it's time to give up on the notion that the healer is expected to save you from yourself. People used to blame this notion on "Wrath babies" who leveled during the last expansion, but we're months into Cataclysm at this point. If you're still doing things like standing in ground effects that give you several seconds warning before they go off, you can stop blaming Arthas' expansion for it.
Positioning is more than just knowing when to move, however. It's also knowing where to stand in the first place. We can see a dizzying array of conditions in this first tier of raiding. The Conclave of Wind requires a raid to be spread out and to switch targets between platforms and deal with adds, while Valiona and Theralion requires the raid to change between being spread out and grouped up as the phases change, while dealing with abilities designed to force positioning changes like Blackout.
There are often adds that must be burned down, kited, burned down while being kited, and so on. Some bosses are council-type fights where you have to switch targets due to a reoccuring mechanic. Knowing what you're supposed to be hitting is very important.
Yes, target switching and high mobility fights are terrible for warrior DPS. (On the other hand, a lot of adds can be pretty good for warrior DPS; you'll just have to figure that one out for yourself.) Warrior ramp-up time is fairly high, and having to move halfway across the room to hit something can cost you rage. That doesn't mean you can leave that to other classes. If there are poison mobs chasing people around during Omnotron and they reach their target because you didn't feel like peeling to hit them, you've just done more harm than good to your raid.
Using all of your abilities
I mentioned interrupts up above, but it bears repeating. Many fights have an ability that can be interrupted. One fight (Maloriak) actually requires a great deal of communication about when you're going to interrupt versus when you're not going to. But in addition to interrupts, as a DPS warrior you have access to Heroic Leap, Charge/Intercept, Enraged Regeneration, various shouts and debuffs such as the Thunder Clap debuff (very easily incorporated into an arms warrior's rotation), and you should be using them to get into and out of combat more easily and to avoid the various death spots on the floor. If you have to kite, using Heroic Leap and Intervene to help you move around the battlefield and get a lead on mobs is greatly helpful, as is Piercing Howl. Even if you're not the one kiting -- heck, especially if you're not -- Piercing Howl is almost always worth using during a kite phase to help out. (It's great for Magmaw's parasites, as an example.)
I am often amazed both when tanking and as DPS with warriors who won't use Enraged Regeneration. Don't be that warrior.
Don't do stupid things
We both know what I mean. Don't deliberately pop all of your cooldowns and a Golemblood before the tank has had time to even say hello to the boss. Don't be tempted to stand in death raining from the sky to get a little more rage for a special and end up dead. Don't stun a mob on its way to a tank and whale on it while the tank is trying desperately to get it where it's supposed to go, ending up with aggro on it. Don't ignore your sound bar on Atramedes.
We all know that this expansion is fairly challenging, as melee DPS goes. We're often in the thick of the worst possible places to be, target switching requires a lot more mobility for us, and our DPS often suffers for making the survival-oriented choice. Don't make it worse for your group by refusing to do anything to help keep yourself alive.
At the center of the dury of battle stand the warriors: protection, arms and fury. Check out more strategies and tips especially for warriors, including Cataclysm 101 for DPS warriors, a guide to new reputation gear for warriors, and a look back at six years of warrior trends.