The movie that Bart and Mrs. Krabappel watch together is a parody of the 1986 film Back to School, starring Rodney Dangerfield. It apparently stars Larry Burns, who was voiced by Dangerfield in the eighth season episode Burns, Baby Burns.
The "Z" in the episode's title refers to Zachary Vaughn.
The Answer book is a reference to The Secret which is a self-help book also turned into a movie.
"Blue Bronco" is an obvious parody of the real life drink "Red Bull".
The song that plays at the beginning of the episode is "Another Day" by Paul McCartney and Wings.
This is the first time Marge and Lisa appear, but have no dialogue.
The blackboard in the background during the Parent/Teacher Night scene between Zachary Vaughn and Homer reads "zackattack.com". This website, that did not exist when the episode was first aired, could be a parody of screwattack.com.
This is one of the few times the end credits differ from the normal ones. In this case the credits are in fancy writing.
This is the first episode in Season 21 to have the normal music for the end credits.
In real life, Tufts University does not have an M.Ed. program.
In the opening, we see Richard is apparently a bad student in Math, having gotten an F.
Martin and Nelson were both given a "B" in the same exam by a very sleepy Mrs. Krabappel - Martin had only one incorrect answer, while Nelson's were all wrong.
This is the second episode where Bart accidentally gets a Springfield Elementary faculty member fired and helps them to get back on their feet out of guilt only for the replacement to be fired eventually. The first was Sweet Seymour Skinner's Baadasssss Song.
When the kids are playing with their cellphones, Sherri and Terri are sitting in the first line. In the last line, there are two hands, similar to the twins' ones, holding a cellphone, but the rest of the kid's body isn't seen.
Krabappel takes the kids' cellphones and keeps them in a box. However, just a second later, when the kids groan, the cellphones are on their tables. Then, they disappear again.