I don't think these have been mentioned yet, so I'm going to dig deep and offer these two cliches that annoy me are:
1) The Noble Idiot: The Hero/ine discovers an obstacle that could endanger their relationship with the Love Interest, and instead of discussing things together, the Hero/ine decides to break up with their LI. Or disappear without a trace. Thus leaving the viewer with an annoying episode riddled with unnecessary angst until the LI discovers the truth and hunts down the Hero/ine, and together they overcome that pesky obstacle. I don't know---some might find it heroic; I just think it would save a lot of hassle if the Hero/ine skipped the noble idiocy and actually, y'know, talked things over with the person they're supposedly fated to be.
2) The Irredeemable Villain: OK, I love a good villain, but to me a good villain is someone whose motives I can sympathize with, and K-dramas can often miss the mark with this one. Specifically when the Villain is found out and confronted by the Hero/ine. Usually the Hero/ine says something along the lines of, "Give up now, and we'll make things easy for you." And the Villain says, "No, I've come too far; I can't stop now." ....What the nonsense?! Now you're just being a jerk for the sake of being a jerk, Villain, and I ain't down with that.
And there're the minor things like: unnecessary terminal illness or amnesia; chaebol moms; conveniently overheard conversations/conveniently witnessing something one shouldn't have seen; not knowing someone's stalking you when they're hiding behind a telephone pole five feet away (I know these actresses are tiny, but come on...).
Re: Oppa. I find the Pouty Oppa-Wiggle to be kind of annoying, but I also find it really interesting since in some cases it's done cheekily to manipulate male characters, so I've come to see it in some instances as equivalent to showing some leg/flashing some cleavage (kind of problematic, yet also kind of subversive). I've spoken to a Korean guy friend of mine about the use of "oppa" in the real world, and he says that it has less to do with defining a direct one-on-one relationship between guy and girl, and more to do with defining the overall role of older men in a younger girl's life, that of guardian. Which is apparently in keeping with the Confucian idea that women are meant to be protected by men. So, a girl can have differing personal relationships with her oppas, but all of her oppas are tasked with looking out for her. I find that interesting when compared to a younger guy's use of the word "noona", especially since in most K-dramas I've seen the younger guy will ask to stop calling his older girlfriend "noona" and to start calling her by her name (in a way this seems to be a leveling of the playing field that's not allowed within the "oppa" relationship). Anywho, there's so much going on behind the whole "oppa"/"noona" dynamic that would probably be better understood if I had been raised in a society built upon Confucian notions of gender hierarchy. I think that before I graduate I need to corner a doctoral student in the East Asian Studies department and have them either direct me to an article about this or convince them to write that article.
Um, right, getting back on topic---cliches I do like. Gratuitous male shower scenes. I also kind of like it when the GUY is all naive and oblivious to the fact that he's in love. I have to admit that some of the magic of piggy-back rides and back-hugs is lost on me. Being kissed on the forehead, however, I imagine is like being sprinkled with fairy dust.