Tommy and his father cross West 73rd Street, which shows traffic going in both directions. West 73rd Street is a one-way street, going east to west from Central Park to Riverside Drive.
In the opening scenes, a jet (a DC-10 with Canadian Airlines International livery) is seen landing at an airport. Supposedly, this is a flight from Amsterdam to New York, but Canadian's service to Amsterdam was to/from Toronto, not New York. Canadian was taken over in 2001 by its long-time rival, Air Canada.
At the beginning, when groceries are delivered to Jessica Fletcher, the grocery delivery boy (Neil Patrick Harris) brings in the grocery box. The name on the side of the box says "Richard's". The store where the delivery boy works reflects a different name, not "Richard's," on the store window. This is not a goof because grocery stores use any available box (normally from a delivery to the store) and not special boxes with their own store name on them. When a later deliver is made, another box with the name Vin Rose on it, happens to be used.