The joke where the police officers laugh at Marge for a long time was pitched by David Mirkin and features a "crazy twist" at the end where Wiggum says "welcome aboard". Mirkin liked the joke so much that he repeated it again at the end of the episode.
The original design of Marge Simpson in the police uniform did not have her hair down, but had her hair as normal with her cap on top of it. But Mark Kirkland thought it would take up too much of the frame, and also thought it would be too humorous, mainly because the portrayal of Marge as a police officer was not supposed to be funny.
The idea to have a counterfeit jeans ring was pitched because at the time there had been an explosion in the jeans market, and David Mirkin thought it was right to satirize it.
After Moe mocks Homer for saying the word "garage," Homer asks what Moe calls it, to which Moe responds that he calls it a "car hole." The way the line was pronounced confused some fans, who thought he was calling it a "car hold." Hank Azaria has clarified on X (Twitter) that the line is, in fact, car hole, and was written in the script as such. He also stated that he needed to enunciate better, and that he gets asked about this at least three times a year.
When the Korean animators were animating the sequence with Marge in the gun training course, they did not know how to correctly animate the "shell com[ing] out of the gun" because guns were illegal in Korea. They had to consult with the American animators, who advised them to watch movies so they could properly animate the guns.