Landon's scar disappears and reappears during the early parts of the movie.
When Jamie receives the paper from Landon to a star he had named for her, she is clearly holding the paper as she moves to sit down. As soon as she is seated, the paper is completely missing from the scene. (This is revealed by the director's commentary on the DVD.)
After the play ends, Landon is being congratulated by Eddie. As Eddie is talking, Jamie leaves the theater and we see Eddie cross in the front of the shot. But he's supposedly talking to Landon at the time and in the very next shot, he's standing in front of Landon talking again.
The day after the play, Landon goes through the library to go to the cafeteria, he has a white shirt and blue vest on. When he goes into the cafeteria, he is wearing a white tee shirt under a green shirt. Then when he is with Eric later, he is wearing the blue and white outfit again.
When Jamie is crossing the school yard carrying a box, and one of the girls says, "Nice sweater," to her, Jamie is wearing a backpack, as evidenced by the visible straps on her shoulders. When she walks away we see her from the back and she is not wearing a backpack.
We see the comet moving. Comets appear still to the human eye and would not pass by stars in a few seconds.
When Landon asks Jamie to show him Pluto, she tells him that it's only viewable just before the Sun rises. The only two planets that would have this distinction are Mercury and Venus.
Pluto is much to faint to be seen with the small telescope that they use (minimum 18" necessary).
The day that the flyer is made about Jamie, all of the characters are wearing exactly the same clothes as they were a few days before when Dean asked Landon if they were still cool. A few days later, when the fliers come out they all have the same clothes back on.
When they made the fliers, the body that they show has some clothes on, but on the other fliers, she doesn't have any clothes on (mentioned in DVD commentary: see trivia).
When Landon and his mother are sitting outside discussing what Landon's goals are, Landon's mother has her back facing the camera and her voice does not match the actual scene.
When Jamie is singing "Only Hope" there is a shot of the piano player. What she's playing doesn't match up to what is being heard.
In the school bus scene, if you look through the back door window, you can see someone in the car following the bus wave.
When Landon and Jamie are setting up the telescope to look at Pluto, what should be Jamie or Landon's hand is the hand of an older man.
When Landon shows Jamie the new telescope for the first time, Landon's wireless mic transmitter is visible as he walks towards the telescope to see the comet.
Beaufort, North Carolina is nowhere near the Virginia state line.
The main characters do not sound like they are from North Carolina, the state of the film's setting.
When Landon and his friends leave the hallway to go to class in the shot behind Landon, you see that Belinda is clinging onto Landon's arm, not fitting in their character relationship. (Mentioned in the director/actor commentary: Shane West says that they were all good friends and left the scene naturally. They didn't realize they were being filmed at the time.)