The Games That Play Us - S1-E22
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.
What Is And What Should Never Be - S1-E20
Continuity mistake: Haley's lipstick gets noticeably thicker and thinner between different shots when she's talking to Nathan (when she drops over some groceries).
The Games That Play Us - S1-E22
Continuity mistake: Throughout the entire episode, Lucas' hair length ranges from being short to long.
What Is And What Should Never Be - S1-E20
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.
Revealing mistake: While Lucas is in the shower and someone steals his towel and clothes, he walks out into the hallway holding two basketballs. When he turns toward coach Durham you can tell that Lucas has on nude colored underwear.
Visible crew/equipment: When Lucas meets Peyton by his tow truck there's a crewmember wearing a green shirt with arms and legs visible next to him.
Factual error: When Lucas writes an email to Karen, we can see in the "To:" box that he typed "karen'scafe@hotmail.com". But the email can contain only letters, numbers, periods (.), hyphens (-), and underscores (_). It can't contain special characters nor accented letters.
Visible crew/equipment: The scene where Lucas meets Payton on the side of the road with the tow-truck. Once they are ready to get into the truck you can see equipment in the middle of the road, as Payton starts walking towards Lucas. (00:28:50)
With Arms Outstretched - S1-E9
Continuity mistake: When Lucas is showing Keith his tattoo, in each shot the sleeve of his shirt keeps changing from rolled up to rolled down.