Both Sides Have a Point: The writers tried to give both sides of the gun rights debate reasonable arguments. Word of God says that if there is any message in the episode, it is that irresponsible idiots like Homer shouldn't own guns.
Call Back: Among the many incidents from Homer's background check are fighting George H.W. Bush in "Two Bad Neighbors" and being institutionalized in "Stark Raving Dad".
Lost Aesop: Marge and Homer are at odds over the gun he buys, which even leads Marge to briefly leave him. In the end, Homer finally agrees to let Marge get rid of the gun, so Marge heads to the nearest garbage bin to throw it out. However, seeing herself holding the gun from a reflection in the lid, she likes how dangerous and cool she looks so she decides to hold on to the gun, putting it in her purse. The writers said that there was no real message from the story, but if there was, it'd be that people like Homer Simpson should not have a gun, so... mission accomplished?
Powder Keg Crowd: Springfield descends into a full-blown riot out of sheer boredom.
Strange Minds Think Alike: When Lisa told Homer the Second Amendment was just a relic, Homer conter-argued that it keeps them safe from the King of England. Later in the episode, when the NRA learned how irresponsible Homer was with his gun, Krusty started berating him by claiming that guns should be used for "family protection, hunting dangerous or delicious animals, and keeping the King of England out of your face."
Take That: The reason the soccer riot starts is because the soccer game is incredibly slow and boring.
Krusty: Come on, you schnorrers, do something!
What Happened to the Mouse?: The soccer riot was never resolved in this episode, and was only there as a cheap set up for Homer wanting to buy a handgun.