The rapper Alcatraaz is a parody of Southern Rapper Ludacris due to his extatic character, faint resemblance to Luda, and gangsta like tendencies (such as when he said he was going to go "murder his enemies")
The clock necklace seen in the footage of the rap concert is a part of Flava Flav's iconic stage costume. However, he does not set it to the actual time, and instead sets it to 3, 6, 9 or 12 o'clock to represent something (for example, 12 o'clock is "straight up").
The jokes about Kirk getting trailer time with Springfield's craziest chicks is a reference to the many jailed serial killers (such as Susan Smith) who have placed ads looking for a partner and gotten thousands of responses.
Chief Wiggum calls Bart "Bratty Hearst" after Bart asks Wiggum not to arrest Milhouse's dad. This name is a reference to Patty Hearst, the newspaper heiress who was kidnapped in 1974 and who eventually bonded with her captors, famously helping them in the armed robbery of a bank.
As Chief Wiggum says "Questions?!?" and pulls off his napkin the shaving cream on his face instantly disappears.
Chief Wiggum tells Barney Fife that his "fat" has grown over his badge. He demonstrates this by lifting the fat so the viewers can see the police badge. However, in the next scene viewers can easily see the badge without Wiggum lifting up his fat.
Lisa says "the truth can't be swept under the rug" but in Lisa the Iconoclast she preserves the lie of Jebediah Springfield due to it making everyone happier.
When Chief Wiggum is examining Bart's recording, it is night but when he, Eddie and Lou go to the Kwik-E-Mart to search for evidence, it is day.