The Fresh Prince Project - S1-E1
Continuity mistake: When Will puts the last of his wall-shaking staples on the Malcolm X poster before the butler's interruption, the poster is almost perfectly flat. When Geoffrey walks to the poster, a bottom corner is noticeably raised. When Carlton walks to it, it's flat again, and raised when Will freaks out at the mirror. (00:07:40 - 00:10:00)
The Fresh Prince Project - S1-E1
Revealing mistake: When Will screams in front of the mirror, imagining himself turned into Carlton, something went wrong making the composite shot and not only you can actually see the line of separation between the two frames, but the superimposed one exposes a bit of the mirror woodframe before it wiggles into the correct position and covers it up. (00:11:30)
The Fresh Prince Project - S1-E1
Revealing mistake: When Will staples his Malcom X poster to the wall, the wall bends back and forth for a second or two.
The Fresh Prince Project - S1-E1
Visible crew/equipment: During Will's first introduction to Uncle Phil the camera tilts slightly down to Will and Aunt Vivian on the couch and the boom mic drops into the frame briefly.
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