Jay Sherman from "A Star is Burns" and series The Critic, makes a cameo appearance in a cell, telling his doctor, "It stinks! It stinks! It stinks!" The doctor responds, to humor him, "That's right, Mr. Sherman. Everything stinks."
The Critic had recently been cancelled, and this was the writers' explanation as to why (The Critic creators Al Jean and Mike Reiss were the show runners when Oakley and Weinstein were hired to The Simpsons staff).
Todd is wearing a Butthole Surfers shirt when the Flanders family is in the relief center ("Look, Dad! I'm a surfer!"). The censors, however, only allowed "Buttho Surfers" to be shown.
Ned says in the church "I don't drink or dance or swear." but in "The Joy of Sect" he is seen dispensing beer in his "rumpus room" and in the Season 2 episode, "Dead Putting Society" he is offering some beer and sandwiches in his "rumpus room".
The Critic – Jay Sherman makes a cameo appearance in the mental hospital scenes. The Simpsons writers joked that this is what really happened to the character after the series was cancelled. Critic fans, however, don't consider this appearance part of the series' canon.
Dick Tracy and Pruneface – Ned's "Prune Tracy" remark is a pun on the comic strip detective. It's also an allusion to an off-color joke: Given the progression, the next name would be Dick Face, had Dr. Foster not stopped him.
Swanson TV dinners – The Juvenile Aggression Study film is sponsored by Swanson Angry Man Dinners, a play on Swanson Hungry Man Dinners.
Halloween - Dr. Foster is shocked to receive news that Ned Flanders has gone mad, stating: "May god have mercy on us all!", referencing Dr. Loomis' reaction to Michael Myers' escape in the first Halloween film. This is clarified on the DVD commentary.
Willy Wonka & the Chocolate Factory - The small door in the rebuilt Flanders house is a reference to the small door in the Wonka Factory. This is also clarified on the DVD commentary. A sign also says "Flandy is Dandy" in the crowd scene at the end, outside the Mental Hospital which may be a reference to the saying from the film "Candy is Dandy but Liquor is Quicker".
The flashback should have taken place 50 years ago, for Ned to be a child. If the flashback took place 30 years ago, Ned would have been 30, since Viva Ned Flanders revealed Ned to be 60.
When Flanders talked to the Lord, he said that he never swore. However in Homer Loves Flanders, when Flanders got disturbed by homer breathing through his nose during prayer, he got up and shouted "BREATH THROUGH YOUR -DAMN- MOUTH!!!" Either Flanders lied or forgot the moment.