Revealing mistake: The actor that played Barney Miller, Hal Linden, was left handed and did everything left handed. However, they always put his gun on his right hip with the handle facing the right. A lefty cannot conveniently pull the gun this way.
Factual error: It is uniform day where they all have to wear their uniforms. The badges they all wear are those of patrolmen. The problem is that they are detectives and the NYPD has detective badges, which are distinctly different looking.