Meh, I don't think of it as art. I think of it as 1) eye candy and 2) a good reason why I don't live in Japan. I completely agree that anime is completely bananas in the plot department, but that makes it a little fun for me. Yeah, it's a pain in the ass learning everybody's name, their family situation, dark backstory, chest hair length, etc. but once you know them it's entertaining to see how messed up a plot can get and still be coherent (with a little effort on the viewer's part, of course), as well as watching people have epic duels with umbrellas and whatnot.
What I DON'T like about anime is that it's either a romantic drama or it's a violent one that suffers from what I call "Dragonball syndrome." Remember how intense the fights were in early Dragonball, anyone? The Goku-Raditz (sorry if I misspelled that) fight was way more enjoyable than watching Frieza and... SOMEONE float above an exploding planet and talk about how the planet was exploding in between yelling at each other and looking surprised at the other's power level. An unfortunate number of violent animes do this; start out with insanely fast, high-quality fight scenes until the art department bitches enough that the director(s) resort to powering-up scenes instead of real combat. That's just the violence aspect of it, though. Character development also tends to go down the shitter from what I've seen, instead resorting to angst that takes eons to resolve any sort of interpersonal relationships. Gah.
Whatever. I still like some animes, for different reasons. I don't call myself a huge fan of it (I may well be in denial about that one), but I still enjoy it.