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she didnt "Figure it out" she remembered him.

Because that would have been far too easy.

Also the Aang running like the wind. He had to airbend to do so, you remember in the episode that Katara and Sokka get sick in, right? He can't run like that normally. As well, he was trying to hit her with attacks, not simply catch her.

When it comes to what they could have done, there is a very good reason why they didn't do it.

Ever get in a fight with someone and after they leave the room, you think of a great retort to something they said?

That's why. It's called a brain fart. In the heat of the moment, you just can't think clearly. I'm sure the gaang had moments after a battle where they were sitting around and someone slaps their head when they think of something they could have done differently.

~

As for Appa, if you were an animal trader and you found a dodo bird, I think you'd be quicker to find the highest bidder rather then return it to the rightful owner. Greed people. It's all greed.

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I forget the episode number, but in the episode where they're discussing if Zuko should teach Aang, there's a pack laying on the ground at their feet while they talk. In the over head shot during the same conversation, the pack is gone, but it's magically back when the camera changes angles again at the end of the conversation.
Once the conversation is over, Aang starts to walk away in the background, but he freezes frame while everyone in the foreground keeps moving. Not an instance of him standing still. He is a still framed image while everyone else moves. As an animator myself, I fully understand that you work in layers, but surely someone noticed they forgot the rest of Aang's animation in the scene.

bato's beads are on the wrong side when he exits the gondola at the end.... in boiling rock

i thought htat the image was the wrong way around but zuko's scar is on the right side... i think...

@The Mei/Mai thing
I think on the Nick site they spell it like Mai on the little character profile things but it's not pronounced that way in the show.

But has anyone noticed this during the Fire Bending Masters?

On the Mai/Mei topic: It's Mai. Why? Because it is. Yes, according to certain pronunciations that's not right. But does it matter? No. Because it's Mai.