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).
Plot hole: When Dan asks Lucas how he managed to lie to Karen about his heart test results then successfully move out, Lucas tells Dan that he showed Karen Keith's test results letter instead. In a prior scene, Lucas hands Karen the results letter and she is elated to read no Hypertrophy issues. Being a very savvy business woman, Karen would have noticed the addressee on the letterhead was Keith, NOT Lucas.
Plot hole: In season 4, Haley finds out she is pregnant. It is presumably around February, since it is right after Nathan and Haley's vow renewals and after the school shooting. If she, let's say, was already a few weeks along, she would not have given birth in June at graduation, but in October of the following year, since it takes 40 weeks or 9 months for a baby to go to full term, not 5 months.