I find the argument regarding sound and specifically art/drawing interesting.
I think that it's a legitimate complaint when an anime has bad art, but that what constitutes bad art may be very close-minded for some people here. The purpose of writing, music, drawings etc is to convey a message. If you don't want to hear that message, not matter how good or well it is being conveyed it won't reach you. Which means if you have a very immediate and negative reaction to any art-style that you aren't familiar with, it could be quite a mental block you're building for yourself that prevents you from enjoying a quality product.
For me when I encounter anything with a very foreign style, be it in art or music or whatever, I try to withhold judgment. Or at least, if that is impossible, I give it a fighting chance to prove itself. No one is immune to the feeling of automatic rejection of new things, but I find if I'm analytical and really try my best to see value in a form, I often do. And really, if an anime has a great story, the chances are even if the art and music is very weird and hard to like at first, it is also very deeply thought of and full of meaning. Something you might not get from your average art style that you're used to.
When you answer the question "What makes anime good?" I think your answer has to be more complex than "Good art!" You have to also answer what you think makes art in anime good. For me, being easy on the eyes, realism, and complexity are not mandatory qualities. They are undoubtably good qualities, but something that is not drawn realistically, something that is even very confusing can often have value buried beneath that you have to connect to the story. I value very symbolic art as well, and it doesn't have to be realistically drawn. It can be very squiggly, sketchy lines, and I will ask myself "Why did they choose to make those lines squiggly?" If I can answer that question, then it is good art. If I can't, then I either don't get it, or there was no meaning to be found in the first place and it is bad.
An example, I guess, is Kaiba. Very strange art style, but very symbolic and interesting. It's off-putting the first 2 episodes, but after that I began to love it. I often like old animes too, because the detail in the backgrounds is always superb, and important to the story and underlying messages of the work. Then I can give an example of say, Clannad, or Jigoku Shoujo... Very normal, very average art style. I really liked those animes, but I wouldn't say the art style helped or hurt them. It was just typical, but I suspect this is what people mean when they say "it has to be good art." It was absolutely mediocre art, despite some powerful images, because nothing could be emphasised in such a rigid style.