Replacing the lead shot in the shotgun shell with sand would actually help the investigation. A shotgun barrel is not rifled with land and grooves, like a rifle or pistol, but is smooth so therefore the barrel would not leave identifying marks on the lead pellets.
Jack Lord appears in the film 2 or 3 times as one of the detectives at police headquarters.
The newspaper Frank tells Mary to look at is the Daily News (New York, New York), dated 16 Aug 1949.
When Dr. Mahan looks up "Fisher Monuments" in the phone book, she says it's on "Gun Hill Road" in the Bronx. However (and as noted here in "Filming Locations") the monument company is actually on East Tremont Ave, also in the Bronx. A wide view taken from inside the yard towards the street when the police arrive shows St. Raymond's Cemetery in the background. This monument company was also used...for a similar shootout between police and the bad guy...by the TV show, "Naked City" about ten years later.