When Lisbon is confronting the suspect, she holsters her gun, but then is shown holding the gun.
Gun laws are by state not federal.
It is claimed that the victim got killed by a 5 iron, but on screen you can see a wood.
Police are allowed to lie during interrogations so when Lisbon is interrogating Yegor and she states that an individual is required to have a license to own a gun in the United States it doesn't matter whether there has ever actually been a law requiring a license to own a gun.