Twilight author Stephenie Meyer once stated that New Moon was her favorite film adaption of the series, owing to its closeness in capturing what she wrote in the book. Whereas Catherine Hardwicke managed to succeed at capturing the spirit of the first book while changing things onscreen for the sake of time, all while putting her own unique artistic stamp on the film, Chris Weitz took great pains to adapt New Moon very faithfully to its source material, both stylistically and narratively.
What resulted is another great adaptation and a continuation of the authenticity of the first, but one that feels markedly different from an aesthetic standpoint. Despite the accuracy of the adaption, some things necessarily needed to be added and removed, either for the sake of time or for the purpose of livening things up visually.
Bella's Birthday Gift
In the books, readers hardly get a mention of Bella's future best friend Jacob Black until long after Edward leaves. She goes to him when she needs someone to fix the broken-down motorcycles she bought, as part of her plan to be as reckless as possible in Edward's absence.
The movie smartly brings Jacob on screen before the novels, so that his friendship with Bella is a bit more established and their later interactions feel more natural. He shows up at her school on her birthday and gifts her a dreamcatcher, another element that isn't in the book, but that sticks around in future films as well.
Jasper's Pretend Age
In the books, Rosalie, Emmett, and Jasper pretend to be seniors during Bella's junior year, while Edward and Alice pose as juniors. In New Moon, Bella, Edward, and Alice are seniors, but the movie changes Jasper's pretend age so that he is in the same grade as they are.
This could be due to the fact that Jasper was seen on the class field trip Bella, Edward, and Alice went on in the first Twilight movie. Another reason for this change could be so that Alice had someone to hang out with at school, rather than constantly third-wheeling with Edward and Bella.
The Cullen's Eye Color
In the books, Stephanie Meyer describes the Cullens, as well as all vampires who partake in their "vegetarian" lifestyle, to have golden eyes, as opposed to the red of vampires who drink human blood. In the Twilight universe, when vampires are thirsty, their eyes are described as turning black, which can be seen in all of the films except New Moon.
For whatever reason, the New Moon movie adaptation forgoes the black color contacts for keeping the gold, even in scenes from the book where the vampires are specifically described as having black eyes.
Bella's Hallucinations
In the books, Bella's hallucinations of Edward are almost strictly auditory. She hears him speak to her when she's about to do something dangerous, which she later thinks is her mind's way of telling her what she hadn't accepted, that Edward still loved her even while he was gone.
The film, being a visual medium, needed to find a way to adapt this visually for the audience, and used special effects to have Edward appear as a ghostly apparition when Bella was hallucinating.
Bella's Awkward Date
New Moon accurately and hilariously captures the awkwardness of Bella's pseudo-date with Mike Newton and Jacob Black, save for the way the night ends. In both the book and the movie, Mike gets sick due to having caught the flu that wiped out the rest of the group that was meant to accompany them.
However, in the book, Jacob quickly drives him back to Bella's house, where his van is waiting. He's annoyed, but not outright furious. In the movie, he responds to Mike's illness by menacingly inquiring: "Feeling sick? Maybe you need to go to the hospital. Want me to PUT YOU IN THE HOSPITAL?" It's a bit of an overreaction, but likely meant to demonstrate a fiery werewolf temper.
The Pack Confrontation
Things also get significantly heated up when Bella confronts the pack for the first time after figuring out Jacob's secret. In the book, she speaks with Jacob first, and they confront the pack together, which results in Jacob and Paul fighting in their wolf forms.
The movie still has this confrontation end with a wolf fight, but it starts differently. Rather than wait for Jacob to wake up and speaking to him first, Bella runs straight out to confront the shirtless, jort-ed young men, who she believes have forced Jacob to turn into a werewolf. She punches Paul in the face, and then Jacob comes in to save the day.
Harry's Death
In the book, Harry dies of a heart attack after witnessing his daughter Leah turn into a werewolf for the first time. Since readers are mostly limited to Bella's point of view, and she doesn't learn about the true reason for his heart attack until Eclipse, this plot point is sort of background in the book.
The movie makes Harry's death happen during an action scene when he and Charlie are hunting the supposed super-bear that Charlie believes is killing people in the woods (it's not a bear, it's a vampire, but nobody can tell Charlie that). Harry sees Victoria while in the woods, and she is about to kill him when Jacob interferes, pulling her off of him. Sadly, the shock is too much for Harry, and this is what causes his heart attack.
The Volturi Confrontation
In order to spice things up for the climax of the film, director Chris Weitz chose to stage an action sequence during the Volturi confrontation in Italy.
Whereas the book just has Bella, Edward, and Alice share a long, tense conversation with the Volturi, the movie has Aro (played by Michael Sheen), the leader, decide to have Felix kill Bella. Edward fights Felix in defense of Bella, and nearly kills him before Bella intervenes and offers herself in his place. This is when the film has Alice show Aro her vision, which is essentially their ticket out of the situation.
Edward And Bella's Reunion
Bella and Edward's reunion in the books plays out differently from the movie in various ways. First, Bella remains under the impression that Edward doesn't love her for much longer in the book. It isn't until she's home and they have a long conversation that she realizes the truth, and even then she doesn't fully accept it right away.
The movies make their reunion a more immediate thing, from an emotional standpoint. From the moment Bella saves Edward in Volterra, they pretty much make out and he tells her he still loves her. They then share a much briefer conversation in her room back in Forks, before they're totally back on again.
Final Confrontation With Jacob
Weeks pass before Bella speaks to Jacob again after her return from Italy in the books. The movie has them talk the next day, when he stands in the middle of the road to get her and Edward's attention.
In the books, he shows Charlie Bella's motorcycle, which he's forbidden her from ever riding, getting Bella in huge trouble. Jacob says he was trying to get Bella grounded so she couldn't hang out with Edward (or rather, he thinks this and Edward says it out loud). The movie forgoes this low blow, and instead just has Jacob deliver a message from the pack.