The song "Calling You" sung by Patti LuPone's character in the bathhouse wasn't released until the 1987 film Bagdad Cafe, 6 years after the action of this episode.
The police car at the harbor is a 1986, not 1981 and earlier, Chevrolet Caprice. The 1986 model is only model year with quad sealed-beam headlamp capsules and aerodynamic scone-shaped external rear view mirrors.
A short establishing shot shows passing subway trains of the R68 class, which were not built until 1986.
Near the beginning, police comment that a body was found by people fishing in the Hudson, but the Williamsburg Bridge, which crosses the East River, is clearly visible in the background.