When in uniform, Captain Miller should be wearing a white shirt, as he is a member of Command Staff. Also, Detectives who attain a rank of Sergeant should be wearing gold Sergeant shields with an eagle on the top, and stripes on their sleeves. The other Detectives should be wearing gold Detective sunburst-style shields on their uniforms.
Listed as "Uniform Days" on the DVD version.
Fleischer's non-delivery of mail would not be a police matter, but would be handled by the postal inspection service, as this is a federal crime.
Just as Captain Miller is wearing his Captains bars on his uniform,
Det. Sgt. Arthur Dietrich should be wearing Sergeant stripes on his uniform sleeve as he is a Sergeant of Detectives.