Well, the most distilled description of the plot of the first season is that Aang, found by Katara and Sokka frozen in ice at the South Pole, travels with their company to the North Pole to find a waterbending master to teach him waterbending, and as they do so, they're pursued by Zuko, who seeks to capture the Avatar to "restore his honor" in the eyes of his father. So, adhering to that would be the utmost minimum of requirements.
The characters I've seen confirmed as being in the film are: Aang, Katara, Sokka, Zuko, Iroh, Zhao, Suki, Yue, and Ozai. Given that it's a film and doesn't have anywhere near as much time as the show did, I won't condemn them for not having other smaller, yet significant characters; that's not to say that they don't have them and I just don't know about it yet. Characters like King Bumi, Haru, Jet, Bato, June, Jeong Jeong, the Mechanist and Teo, and Pakku are significant in the show, but I wouldn't be too disappointed if we don't see them.
Finding Aang is important, and the trailer has that, so that's there. The realization of how badly the Fire Nation has torn up the world in his absence is critically important, so I hope to see Aang's return to the Southern Air Temple. Suki's in, so a stop by Kyoshi Island is in. Aang needs to learn about the return of Sozin's Comet, so I would hope a stop by the fire temple is in the film. We'd need to know why Aang was frozen in the iceberg and how Zuko got his scar, but we wouldn't necessarily need to have that information presented the same way that it is in the show. I would think that the Blue Spirit would have to be included in order to provide the basis for events to come in the second and third films, but if they work it differently, as long as it works logically within the film's structure, I'd be ok with that. As much as I like Jeong Jeong, I could see them leaving him out. Given the way the events of The Day of Black Sun unfold, it would be difficult to leave out the Mechanist, but I guess they might could find a way to get around him. And the big damn ending of the season during The Siege of the North is so damn big, I can't imagine that they'd leave out much of the three final episodes of the season.
One of the biggest, most important elements to the story is the way the characters interact with each other. Aang and Katara; with Katara finding Aang, Aang's feelings toward Katara, Katara placing her hope in Aang, and Katara's eventual position as Aang's waterbending teacher. Katara and Sokka; their relationship as brother and sister, Sokka's dedication to protecting Katara and Katara's having filled the void left by their mom dying. Zuko and Iroh; Iroh considering Zuko to be his surrogate son given how Zuko's father treats Zuko and how Iroh lost his own son, and Zuko's progressingly realization of how important Iroh is to him. Aang and Zuko; Zuko's relentless pursuit of Aang and Aang's ability to care about Zuko's safety/well being despite Zuko's attempts to capture Aang. I think those character interactions are the most important to keep intact regardless of any specific plot adjustments for the sake of adapting the story to the movie medium.
