When chasing somebody, you want to go W-E-W, rather than W-W-E. The reason for this is that his shadow E has a slow, but Zed's E doesn't. Similarly, when harassing somebody with your shadows, going W-E-Q will make your shuriken easier to hit.
Like Rappel or Alpha Strike, Death Mark allows you to dodge pretty much everything if you can time it correctly. One of the reasons Zed is so difficult to 1v1 is that, with proper timing, he can essentially negate most champion's most powerful abilities. Going into a game, think about the champions you're playing against, and if any of them have abilities that it'd be worth using Death Mark on. If the enemy team has a Vi or Fizz, consider holding on to your ult until they've used theirs.
Also, it's incredibly important to use Tab to monitor your enemy's itemization. Once somebody buys Zhonya's or QSS, you can't use your ultimate on them (until they've used their actives, at least). Getting Zhonya's baited is pretty much the worst thing that can happen to you as Zed. Keeping tabs on enemy summoner/item cooldowns will let you target much more effectively in teamfights.