Misuse of Death Grip
If there's one complaint about DPS death knights I hear time and time again, it's probably this. Death Grip is an amazing tool that can help make fights simpler and easier to survive, but it's also a potent agent of chaos that can sow discord and make everything harder. The latter happens enough that DKs sort of have a rep from it.
Death Grip's main issue is that it both moves a mob from where your other group members are expecting it to be and taunts the mob so that it attacks you. If you're the tank, this isn't generally a big deal. You're the boss of the group, and you know (in theory) how to best position the mob so you can keep its attention.
If you're DPS, however, this can cause issues. If you pull the mob, the tank won't like that you're stealing their job, and you may mess up whatever pull methods they use. When you use it on a mob, you will taunt it, and though you may have the armor to take a few hits, you'll still be soaking up healing your healer could be using elsewhere, and they may not like you for it.
That said, there are certainly good reasons for DPSers to use it. Use it to pull a mob off the healer once it's obvious the tank isn't doing his job. Use it as an emergency interrupt on a caster if your other interrupts are down or otherwise unavailable. It also can help to ask your tank if you see a place where it may be useful to use Death Grip -- that way, your group at least expects that its coming.
For a more in-depth picture of when to use Death Grip, check out this back issue of Lichborne.
Misuse of Army of the Dead
Army of the Dead is one of our coolest buttons, no doubt. You get to summon your own army of lackeys who will fight to destroy your enemies. You become a true general of the undead, your own little lich king.
Unfortunately, this ability is more complicated than it first seems. The big issue is that these ghouls will run everywhere, and they will taunt. That means that they will pull mobs off the tank, they will drag these mobs everywhere, and they do have a chance of pulling extra mobs if you're fighting in a crowded area.
Generally, that means you probably shouldn't summon Army of the Dead unless you're looking at a possible wipe. Then, the ghouls' taunting action can help soak some damage while you try to recover (or at least try to burn down as much as possible before everyone dies). Other than that, you're playing with fire almost every time you summon your army. As a general rule of thumb, if the mob can be taunted (and almost every mob outside of raid bosses can), make sure it's OK with your group before you summon.
For a more in-depth look at the ins and outs of Army of the Dead summoning, be sure to check out this past Lichborne column.
Not using defensive cooldowns
As a death knight, you have a lot of defensive cooldowns, especially if you're tank-specced. There've been stretches of the game when we've specifically been known as the cooldown tanks. This moniker has fallen out of use with the more recent emphasis on mastery, but we still have those cooldowns. Here's a secret: If you don't use those cooldowns, it's basically like you don't have them. If you don't use them, chances are you are not playing your class to the fullest.
At the most basic phase of cooldown use, casting Bone Shield before every pull is a good place to start. It's a long-term, sustainable damage protection buff, and if you have a decent amount of avoidance, it will stay up through a surprisingly large portion of the fight. At the very least, it gives your healer a little breathing room while you spread diseases and set up to start using Death Strikes.
Icebound Fortitude is your next big cooldown, and this is one you can probably safely use as a tank almost every time it's up and you're in the middle of a battle that won't end before its duration finishes. You can then save Vampiric Blood for the periods where you're taking very heavy damage and Anti-Magic Shell for big windup magic spells or a channeled magical AoE.
DPSers, don't think you're off the hook here. If you're going to take some damage, consider hitting Icebound Fortitude or Anti-Magic Shell to take some heat off your healers. Sure, you'll "waste" a GCD and/or a bit of runic power that you could have used on a DPS move, but if you die, your DPS will go down to 0. If you're unholy DPS, you'll definitely want to do this, since Anti-Magic Shell can be talented to provide you with extra runic power.
Not using offensive cooldowns
As a DPS death knight, you will have useful offensive cooldowns depending on your spec, such as Pillar of Frost and Raise Dead for frost and Summon Gargoyle for unholy. You should keep track of these cooldowns and use them, because if you don't, you are leaving DPS on the table.
It's tempting to save the cooldowns until you are fighting a boss or your buffs are all lined up, and sometimes that can be nice if you need a burst of damage. If you know you'll be coming up on a fight where you need some burst damage, sure, save the cooldowns. For example, if I know my mage is going to cast Time Warp during a fight, I'll generally try to pop Pillar of Frost and Raise Dead just after she does, because I know that's going to bring out a much more powerful ghoul to add some extra damage. Just don't leave those cooldowns inactive for too long, or you will be losing DPS. Saving for a rainy day just doesn't work if that means your cooldown buttons are gathering dust.
Leaving resources on the table
If you look at most guides on death knight endgame DPS rotations, you will notice that they'll put up a priority system that, at the top, tells you to use a certain move if you are full on runes or full on runic power. This is for good reason. Your runes are constantly regenerating, and your runic power is constantly filling based on the moves you pull off. If you leave your runes off cooldown, or your runic power capped, you're missing DPS opportunity.
Tanks don't have to worry about this one as much. Tank DPS can be helpful, but it's more helpful to sometimes keep runes pooled for emergency moves. As a DPSer, however, one of the most important things you can master is keeping your runic power spent and at least one rune of each type on cooldown at all times. If you do that, you'll constantly be regenerating resources, which means you'll have more resources to use over the course of the fight -- so you do more damage.
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.