When the dead woman is found in the bath tub James Caan's character Det. Reilly says, "You don't need a laser to connect the dots." The movie was supposed to take place in 1949. The laser was not invented until December of 1958, nine years later.
After the police find the blood under the floor boards in Fernandez's house, we hear Hildebrandt's voice-over that the cops just missed the couple as they were 5 miles away in Seaford, NY buying a flop top car. Fernandez's home was in Valley Stream which is close to 20 miles away from Seaford, not 5 miles.
When the aircraft is shown landing at Albany, you see a runway and taxiway sign that were not in use until decades later.
When the aircraft lands at the Albany, NY, airport, a runway sign indicating Runway 28 is seen. Albany has four runways, none of which are runway 32. The closest runway to that is runway 28.