RE: Avatar
I think most the miyazaki nods are obvious and you're just toying with me
Obviously Appa is a variation of the Catbus with a bit of a totoro style face. There are a few other miyazaki-ish character designs, but by the end of season 1 there are some heavy Mononoke nods. In fact, it is funny how the culmination of season 1 very much has a Mononoke bent, while the culmination of season 2 seems to borrow the feel of Empire Strikes Back.
All that said, before I go further, let me say that SPOILERS ABOUND in the following paragraphs.
Yes, I said SPOILERS. SPOILERS, SPOILERS, SPOILERS! Do I need to say it again, I hope not.
So, yes--in season 1 the whole 'killing a god/spirit' thing felt very Mononoke to me, and the design of the giant monster koi that Ang turns into seems to be inspired by the Spirit of the Forest from Mononoke:
These may feel similar in motion than in their actual appearance. I definitely don't mean to imply one is a copy of the other, but there was definitely a feel of Mononoke that I was really enjoying. Mind you, it still felt VERY original.
The whole connection I am making with season 2 and Empire Strikes Back is occasionally very direct, but often only perceived--and certainly dependent on the way you read Empire Strikes Back. To begin with, I don't really care too much for Star Wars, but I love ESB for dealing with some pretty heavy and universal themes. The 'scoundrel' seeking redemption, the hero who must choose between his own 'spirit quest' and saving his friends. Even the nearly impossible struggle against an all-powerful 'empire'. All these themes are present in 2nd season of Avatar, but of course Avatar has its own twist on the matter; yet the emotional connection to Luke's betrayal and near destruction at the end of ESB definitely seems to be the sort of stuff that this season is made out of. And there are so many betrayals!
Obviously the most direct nod is when Aang choses to step away from his training to save Kitara--and this is done with the knowledge that it might make it impossible for Aang to win the war, and may even cost him his own life. Does Aang promise to return? I don't remember.
Of course, once you are thinking ESB, you can find more connections. You might see some parallel between the conspiracy of the Ba Sing Se and those of Cloud City, but I think that's a stretch. I do however feel the parallel between how the characters in ESB split up, and when they do so, they become weak and the empire starts picking them off. That too happens in Avatar.
All that said however, Avatar does so much more than ESP. These are just nods after all. Familiar and ready motifs to be used for their emotional effectiveness. There's nothing in ESP that gets at all close to moments like when Uncle Sokka leaves a small offering for his dead son, or when Appa returns to the deserted earth temple alone, lost and afraid. That and whatever this series is doing with Suko...wow, that's one of the most redeeming things in the show.
Oh, and lastly, to turn this into a MEGA-POST, I totally agree with you about how they feel free to change up the characters' wardrobes. Very often this seems significant, telling us of some change in the character. They use it effectively!
Anwyay, what a fantastic series. I'll have to be patient for the whole thing to come out!