In the commentary, it says that the Child Protective Services male officer was based on a teacher the writers had.
In the original airing, Milhouse mentioned the basket with the infected monkey in it came from Pier One. After Pier One complained about the joke, the reruns changed the line to Trader Pete's. Later syndicated reruns, FXX reruns, as well as the Complete Seventh Season DVD print and the streams from FXX's Simpsons World retain the original line, though the closed captioning/subtitles have the "Trader Pete" line instead of the "Pier One" line. In the UK, the Trader Pete line is used, as there are no Pier One stores over there.
In the parenting class, Agnes Skinner said that the state was threatening to take Seymour away because they had another fight over the inflatable bath pillow. They first fought over the bath pillow in the episode "The Springfield Connection" from the previous season.
It is revealed in this episode that Marge microwaves Bart and Lisa's underwear on cold days and Homer calls radio stations and gives them fake traffic hints.
Maggie liking Ned would later be referenced in "Labor Pains", when she imagines she's bouncing on Ned's knee.
Maggie says her second canonical word in this episode, in which she says "Daddily-Doodily!" while inside the Flanders' car with Bart, Lisa, Ned and Maude. Her first canonical word was in "Lisa's First Word" when she said "Daddy". However, in this episode, Yeardley Smith (who does Maggie's speaking and other non-pacifier sounds from seasons 1 to 18) does the voice of Maggie speaking instead of Elizabeth Taylor.
In the parenting class, at one point a male with spiked black wrist-bracelets and a shaved head, much like Kearney Zzyzwicz, but seen only from behind and with a black t-shirt. Later on it would be revealed that Kearney is a father.
Initially, Marge puts a purple box of Krusty Flakes near Maggie in the opening scene. The box turns green in an overhead shot of the kitchen, and is instead near Lisa in another shot.
Lisa comes home with trash bags on her feet, but Bart comes home wearing a potato sack and is barefoot. Unlike Lisa, Bart does not have prescription shoes.
Also, how did Lisa get her shoes back?
When Ned is warning Rod and Todd not to poke each other with sharp objects like Itchy and Scratchy, his moustache is totally smooth for a frame.
The social workers demonstrate significant incompetence in their deductions - despite being summoned by Principal Skinner they are completely unaware that the condition of Lisa and Bart is entirely due to events at school. And of course they told Marge she had better have a good excuse, but didn't actually wait to hear it. Nor did they question the children, or Grampa Simpson. The evidence is purely circumstantial. On the whole, I'd be more shocked if a kid didn't catch lice at some point in their childhood.
Realistically, the kids would have been sent to separate foster homes.
Also, sending the kids in the Flanders' home violates the 100-foot restraining order that Homer and Marge were given against the children, and even if the restraining order wasn't in place, the kids shouldn't have been put in a foster home next door to their parent's home.
If Homer and Marge wanted to call the kids, they could have simply gone to a payphone.
When playing a religious trivia game, Maggie somehow gets a question right despite being unable to talk, although this may have been done to emphasize Bart and Lisa's lack of knowledge of the topic. It is possible that she nodded her answer.
The Flanders have both "fire" and "police" on speed dial, even though they are both 911. This is probably a reference to the Flanders neurotic nature
Lice is more a minor inconvenience than a failure of parenting. However, Springfield does have weird and pointless laws.