Other mistake: In the last episode of season 1, Lucas goes to see Haley and Nathan where they tell him they got married last night, which must have been after the playoffs game. However, in season 2 in flashbacks of their wedding they got married during the day.
Plot hole: How in the world could Keith be hired as a teacher? Not only is he a college drop-out with no teacher training, Dan mentions just an episode or two earlier how Keith is incapable of using modern machinery (specifically saying how every high school graduate will be more qualified than Keith).
Deliberate mistake: After the party, in the scene where Lucas goes into the cafe, he finds Haley crying. The shot is a distant shot with Lucas and Haley in it. Haley's hands are covering her face. In the next shot, just of Haley, her one hand is over her forehead.
Factual error: When Lucas writes an email to Karen, we can see in the "To:" box that he typed "email@example.com". But the email can contain only letters, numbers, periods (.), hyphens (-), and underscores (_). It can't contain special characters nor accented letters.