Visible crew/equipment: When Jazz says "oops!" the stage lights are reflected in his glasses.
Continuity mistake: When Hilary starts crying, Tyrone is wearing an apron. In the following shot he is suddenly not wearing it, but in the next shot it is back on. (00:12:55)
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)
Fresh Prince After Dark - S4-E9
Visible crew/equipment: In the episode where Hilary poses for Playboy, Hilary's strap-on mic is visible on the back of her red dress when she, Will, and Carlton first enter the Playboy party. It is gone in subsequent scenes.
Burnin' Down the House - S6-E1
Continuity mistake: Right before Will pours the liquid into the pot, you can plainly see a fire extinguisher on the counter behind him. It's gone when the fire is actually burning.
Burnin' Down the House - S6-E1
Continuity mistake: The cognac bottle is almost empty when Will passes by the counter, but when he turns around to pour the liquid, the bottle is full.
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