Other mistake: When Will confronts his mother about not wanting to move back to Philadelphia, she mentions she can't afford to send him to an out of state school. However, in season 2 it's already been established that Uncle Phil is Will's legal guardian, and he's a resident of California. Will's mother has it backwards. Going to school in Pennsylvania would be an out of state school and staying in California would be in state.
Continuity mistake: Will's hat from his school uniform keeps changing from a snap back to a strap-back in each scene he's wearing it. (00:10:00 - 00:13:00)
Answer: Because Carlton is naive, trusting, and optimistic. He lived a pretty sheltered life in Bel-Air and just doesn't think police officers would do anything unjust. At this point in his life, he just hasn't gone through the things Will has to make him think otherwise.
Bishop73