Homer walking onto stage and saying 'Good Evening' is a parody of Alfred Hitchcock, who frequently introduced his TV series in this manner.
It is the first episode in the series of Treehouse of Horror episodes to have a zombie-related segment. The second is "The Fright to Creep and Scare Harms" in "Treehouse of Horror XIII".
In segment 'Clown Without Pity' the Springfield children are dressed up in their Halloween costumes, Bart appears in 'A Clockwork Orange' costume dress as 'Alex DeLarge'.
After seeing Homer run naked through the kitchen, Patty declares that she just lost the last lingering thread to her heterosexuality. 12 seasons later, the episode "There's Something About Marrying" reveals that Patty is a lesbian (despite that she and Selma have a crush on MacGyver) and always knew that she was gay ever since she was a child.
The names used in Bart's spell book:
Cullen, Rayburn, Narz, Trebek (last names of game show hosts)
Zabar, Kresge, Caldor, Walmart (names of inexpensive department stores, with Zabar and WalMart being the only ones as of 2012 still in business, though Kresge is now known as Kmart)
Kojak, Mannix, Banachek, Danno (names of 1970s TV detectives)
Trojan, Ramses, Magnum, Sheik (brand names of condoms)
Costumes at the Halloween party:
Homer - Julius Caesar (until his toga rips on a nail)
In the scene where Bart attempts to resurrect Snowball I, human zombies arise from around them, despite them being in the pet cemetery. Though some citizens might be cheap and classify their recently deceased loved ones as pets (or the spell Bart chanted was meant to resurrect human zombies and not animals).
Homer's toga was ripped off when he came down the stairs ("Behold, mighty Caesar! In all his glory!"), but when he ruins the evil witch game by eating the food used as the witch's body parts, Homer is in his normal clothes (white shirt and blue pants). Then when Homer tells his crummy ghost story when the show comes back from commercial break, he's back in his toga.
In "King Homer," the spinning newspaper that announced Marge marrying King Homer had Woody Allen's birthday as a sub-story, but when the spinning newspaper is shown in full, the Woody Allen birthday story is replaced with Dick Cavett (and both stories have pictures of what each man looks like as an adult, despite that they were just born). This is most likely a deliberate gag.
In "Clown Without Pity" when Homer yells, "The doll is trying to kill me, and the toaster's been laughing at me!", his mouth doesn't move. Also: the kitchen table is gone.
Marge finds the customer service number for the Krusty doll on a box, despite that Homer bought the Krusty doll at a curious shop owned by a strange Chinese man and it clearly wasn't in a box when he bought it.
Baby's First Pop-Up Book should, technically, be 52 pages, since there are 2 pages for each letter.
In "Clown Without Pity" when Homer is buying the Krusty doll, it doesn't have a box, however when Bart opens the present, it's in the box.
In the ending of Dial Z For Zombies, the securiy guard to the right of Mayor Quimby have a dark skin. In the next shot, his skin is yellow.
The first segment, 'Clown Without Pity' is an overall spoof of the Twilight Zone episode, Living Doll. Coincidentally, Telly Savalas (who is also bald) plays the father in the Twilight Zone original.
The Springfield Shopper's November 19, 1936 issue includes an article "Dick Cavett Born." Cavett was actually born on that exact day.
The title 'Dial Z for Zombies' is a parodic of the title 'Dial M for Murder.'
One of the books Bart picks out when told to redo his book report is "Find Waldo Yet Again," a spoof of the Where's Waldo (renamed Where's Wally in the UK) picture book series.
The Necronomicon Bart finds spoofs annual Time Life Magazine endorsed releases of historic and culturally significant media.
In the Pet Cemetery, there are 3 tombstones that read "Fish Police", "Capitol Critters", and "Family Dog" respectively. This pokes fun of 3 animated shows of the same name that were short-lived.
When Bart raises the dead, he's wearing a Michael Jackson record on his head (coincidentally, it's the Thriller album).
When Bart makes the dead raising chants, some of the names he utters include (Alex) Trebek and Wal-Mart. He then mentions the names of famous TV detectives - Kojak, Mannix, Banacek and Dano - in the spell that turns Lisa into a snail. And when turning Lisa back into human form and getting rid of the zombies, he mentions condom brands - Trojan, Ramses, Magnum and Sheik.