The first segment is a pastiche of numerous Alfred Hitchcock films. The main plot derives from Strangers on a Train, where two men plot to kill off each others' enemies, while other elements of North by Northwest, Vertigo and other Hitchcock movies are included. Hitchcock himself is shown in a brief cameo stepping out of a bus (as he did in the title sequence of North By Northwest).
The second segment is a parody of both 28 Days Later (a pandemic causes mankind to turn into zombie-like monsters) and Children of Men (a society on the brink of collapse due to chaos has one chance of survival thanks to someone with a medical anomaly (in Children of Men, it was the last woman on Earth who is able to have a baby (as all the women in the world in Children of Men suffer from infertility); in Don't Have a Cow, Mankind, it's Bart's immunity from Krusty's latest burger). Also Bart's immunity may be a reference to the sequel to 28 Days Later, 28 Weeks Later which involves certain people immune to the virus.
If you look very closely you can see that the theater reads Madea Goes To Hell.
In the opening, the bullies are wearing costumes of John 117, The Joker from The Dark Knight, and Black Suit Spider-Man from Spider-Man 3.
The first segment title is a parody of "Dial M For Murder", the second segment title is a parody of Bart Simpson's catchphrase: "Don't have a cow, man", and the third segment title is a parody of "There's No Business Like Show Business".
In the second segment, when Bart and Homer initially step outside and Homer blows their cover, Kirk Van Houten is seen in the back right of the muncher mob breaking down the front door to try to get to the Simpsons. Yet, when they make it to the safe zone, Mr. Van Houten is clearly seen in the front of the crowd before the Simpsons push themselves through. While it may be a goof, it could also be someone similar to him, though the physical features are astonishingly alike.
Ralph Wiggum is seen as a muncher eating his own arms. Yet he is seen happy and healthy at the end of the segment. Of course this could mean that Bart's immunity also doubles as a cure for the already infected. You can see Homer is still in his "muncher cage" behaving like a muncher.
After Homer becomes a muncher the gun turns into a single barrel.
In the 2nd segment, Apu explains that he hadn't become a muncher because he's a vegetarian, but in Lisa the Vegetarian he stated that he doesn't eat any food that comes from an animal. This would make him a vegan, not a vegetarian.