I found a lot of mistakes within the movie both central to the storyline or otherwise.
First, the acting was bad. I usually don't notice any caliber of acting but even I could tell that no one was putting any feeling into their lines. There wasn't a lot of emotional variance in delivery which was really annoying. Probably the best example of this is Sokka's line when Appa's tail falls on him-- it sounded monotone and flat when it was supposed to be a joke. Not only was there not a lot of emotion in the acting but none of the actor's faces ever changed either. Aang could only alternate between stoic and surprised and Katara and Sokka could only manage worried and angry. Zuko was the classic evil villain that could only scowl and scowl some more.
The storyline also felt really rushed to me. First we're in the Southern Air Temple and then it suddenly switches to some random Earth Kingdom village? I'm amazed that the movie lasted two hours. I didn't mind some of Katara's narration but, especially when it was used in the Northern Water Tribe, it just felt like a cheap shortcut.
The bending was also really bad. The styles of bending are inspired by martial arts but what makes it look so real in the cartoon is that the bending and martial arts are done at the same time. It just looks really awkward when you have five different moves before something happens. Since this is a live action movie and we have the wonders of special effects I would have expected the movie to look better but no. I also found the 'fire benders can't make their own fire' really lame. Fire benders were strong like that in the first place which was why they were so feared. As learned throughout the series though any bender who can think on their feet has a good chance of defeating someone who can make fire from their fingertips.
Okay, I know this is really old hack but I still can't get over how different the characters looked from their cartoon counterparts. Maybe the director wanted racial diversity in his film. Okay, that's fine, do that for the extras. But was it really necessary to make an asian monk african american? I have nothing against other races or ethnicities but when the characters don't even look like the originals I get a little annoyed. And these weren't even that great of actors either so I'm wondering why they chose these people in the first place.
My biggest disappointment in the movie has to come from the climax. I mean, in the cartoon we get this amazing big fight at the end that makes the whole season worth watching. While I didn't expect Koizilla I did at least expect some serious Avatar State butt kicking. Imagine my surprise when all we get is a giant wave and the fire nation ships magically turn around! Okay, the fire nation is headstrong and crazy, they had a commander who wanted to kill the moon for God's sake, they would not just turn around and leave after some giant wave. I realize that Aang was told not to kill anyone but I have two problems with this: one, this pretty much destroys the future personal conflict he has later in the series about whether or not to kill Firelord Ozai and two, the fire nation doesn't give up that easy! It just seemed like an a cop out ending used to save time.