As a person who has never cosplayed before, but has seen a lot of it, I have one big pet peeve that I always bring up: Don't have an impeccable, unworn, 100% clean costume.
Almost all clothes you wear regularly have wear and tear; stretches, fraying, dirt patches, discoloration and abrasion - often on a small level you don't even notice. Game and movies characters shouldn't be any different, especially if they are a character who regularly gets into rough scrapes and combat. And yet at conventions, Altair or Lara Croft cosplayers's look like they never have never worn their outfit before (because they probably haven't). It sticks out like a sore thumb. No one wants their expensive ensemble damaged, but if you want to make it look authentic, you're going to have to screw it up, kick it around on the floor, wear it and roll in the dirt, and scrub it in water/washing machine a few times. It'll look way better. Interesting factoid: spies do the exact same thing whenever they had to wear disguises - nothing looks more out of place than an unworn uniform.