Carl's police attire (both his patches and badge) are not the ones of the Chicago Police Department. Carl's patches are generic with 'police department' on them. Actual CPD patches are white and octagon shaped and say 'Chicago Police'. His badge is a generic oval shape style like the ones of LAPD. Real CPD badges are 5-point silver stars.
When Urkel has his fantasy sequence, when he pulls his super moves, he kicks the guys gun out of his hand, and the gun clearly shoots a blank, as the yellow color gives it away. Not only is this impossible in real life, but why would Urkel imagine a gun with a fake bullet, and was clearly done for actor safety and not realistic depiction of a gun.