Poor grammar - more in writing than in the spoken word. Run-on sentences annoy me when it's obvious there should actually be two or three sentences in there. A total lack of punctuation or capitalization. And finally, people who type 'leik dis bcuz its quikr omg lololo' in situations where you have unlimited space and time to type things out properly. A 'lol' or an 'omg' by itself is harmless (I do it), but if it's all you're typing... Oh, and THE CAPS LOCK OF DOOM. That's just rude, and it looks like you're shouting the whole time.
Getting away from writing, there's people who let their children get whatever they want, particularly when it comes to pets. At work, I'll be trying to explain that the animal will mostly likely DIE if I send it home with them if they're not prepared to care for it, and the customer will get all pissy because they don't want to spend money but they "promised their kids" they could have a pet. Well, don't make promises without learning what you'll need ahead of time, then!
A lot of things people do with pets annoy me, really, especially when it also comes to my job: impulse buying is a big one. Returning an animal because their kids got bored with it, even though we told them not to get it unless the parents were willing to take up the responsibility if need be. Refusing to go to a vet because "vets are expensive," even if the pet clearly needs to see one, and expecting me to make it better. And taking animals out of the wild. That last one makes my brain hurt the most at times. Nineteen times out of twenty, it's just a bad idea.
And finally, people saying blatantly insensitive or sexist things and acting like those are completely fine things to say. After helping a guy out and finding that his wife hadn't made precise specifications as to what he needed to get, he said he'd just come back with her because she was picky. Not so bad. But then he goes ahead and says, "You know how you women are." What. The. FUCK!?