Them ugly children at the beginning of TP annoyed the hell out me. It was not just the appearence, but they were so horrible to the other guy (Sorry for forgetting the names, I havn't played TP in a while).
What annoys me the most would probably have to be the beeping sound when your health is low. it would always annoy me when I was playing Late at night. Hey, at least it kept me awake with its annoyingness.
Most annoying is probably the sailing in Phantom Hourglass. I rather enjoyed sailing in the Wind Waker, if felt free and open - even if it could be boring at times.
However, sailing in Phantom Hourglass felt like the antithesis of the Wind Waker, it was constricted, limited, the process itself was irritating (I detested having to open the sea chart, draw a line, then sail there. Why couldn't I just.. sail there? It felt like such a hassle.)
Perhaps almost as annoying, was in Twilight Princess. Where every damn time you get a blue or higher rupee, Link has to present it to you like it's something he's never seen before, and act surprised every time - even if you've found that denomination a hundred times already. This wasted so much time, and just overall annoyed me.
The low-hearts indicator didn't bother me too much.. Except for a few times when I got down to one or two hearts, and had to run across the entire field or something like that just to get it to stop.
What annoys me? Well, if it ever happens, the beeping when health is low. The most obvious would be Navi. Obnoxious little fairy. -.-; Then I get a little annoyed by the slow cutscenes sometimes when I know what the say and just want to get along with it.
Hmm...the ReDeads also bug me if I accidentally get too close and they decide to scream and make me stop moving, then they won't get off and baaah...
Really, there isn't too much that annoys me, really.
I find Keese and Wall/floor masters the most annoying. Especially floor masters, they grab you and you have to start from the beginning of a certain point in the dungeon. Second is the magic meter. Upgrading that thing is tedius in all Zelda games with the exception of OoT. Plus, you can only use your magic until it runs out and then you have to smash pots. The Earth temple in Wind Waker was a pain, you had to rotate the mirrors to reflect light and everything. Heart beeps yes, but you can always mute the volume.
Oh wow, so many things. First Navi, never liked her. Then the owl, so pointless wish I could just skip him. And last thing is the beeping when you are low on health, this could be worse though... At least the screen does not blink red or something like that.