The gunman confesses to the crime, but his confession is thrown out on the grounds that the suspect's mother invokes his right to attorney by informing Lt. Buren she had called a lawyer and they had no right to continue questioning him. The suspect is not a minor, and no one else can invoke any of his rights on his behalf. As he had been informed of his rights and chose to waive his right to an attorney and right to remain silent, his confession was perfectly admissible, and the police had every right to continue questioning him.
For guns that can be converted from semi-automatic to full automatic, the purchase of a conversion kit follows the same rules as the sale of an automatic weapon, which requires a FBI background check.
The tracing of a gun from the manufacturer to a wholesaler to a gun dealer to a purchaser is conducted by the BATFE (then ATF when the show was aired) and not by local police since all the information is on ATF forms. Furthermore, Congress has prohibited keeping those forms and the information contained in them in any electronic form so a simple search of a computer would not yield the results. However, in the case of a mass shooting, the BATFE does prioritize the sale tracing and the chain of custody is quickly established.
Interstate gun sales can only be made by Federal Firearms Licensees (FFLs) to an other FFL. Anyone transferring to a non-FFL is likely to lose their license.
In 1999, gun manufacturers were still subject to civil lawsuits. Manufacturers are now immune from prosecution for any crimes committed by owners of their weapons by the 2005 Protection of Lawful Commerce in Arms Act.
On the witness stand, the gun criminal references two school shooters (Columbine) that used semi-automatic rifles. He testifies he needed a fully automatic gun to do what he wanted to do. This is a common TV misconception, as firing a gun on full-auto is the least-accurate means of hitting a target. Aimed single shots against a group of people would be far deadlier (and take only slightly longer) than full-auto fire, as the muzzle rises due to recoil. Firing on full-auto would result in a majority of the bullets going into the air above the people.
Lennie tells Ed that he doesn't like nicknames. But it has been established that Leonard is his given name.