Stabler watches a home movie of his father and his partner teaching Stabler how to shoot when he was a young boy. The video shows Stabler standing in the courtyard of a building, clearly inside the city. Discharging a firearm within city limits is not only reckless and irresponsible, it is also illegal. A police officer would certainly not take his kid shooting in the middle of the city, especially considering the fact that police officers have free access to the department shooting range.
Stabler finds the evidence from the shooting his father was involved in at the NYPD evidence garage, including the pistol supposedly used by the perp. However this case is 40 years old, unless the case it pertains to remains unsolved evidence is not kept for that long, police departments simply do not have the storage space. Typically evidence for a case that is closed is kept for five years past the closing date, then it is destroyed.