The song playing during the baby-proofing montage is '"Always Safety First" by NRBQ.
In the flashback when Homer and Barney are bullying Smithers, Homer is singing "Kung Fu Fighting" by Carl Douglas.
Twice in the episode, Milhouse makes a reference to a poorly-received sequel of a well-received movie (Speed 2 and Babe: Pig in the City) both times implying that he is unaware of the riginal movie.
Waylon Smithers had braces and used to have brown hair in elementary school (meaning that the hair he has now is grayed, despite that the "138th episode spectacular" clip show stated that Smithers is 40 years old, though he could be genetically predisposed to have gray hair before he hits old age).
We learn that Homer was a bully in elementary school, and the kid he beat up would later be his boss's assistant.
We see Lisa wearing her lavender tank top and underwear for the first time in the show. It is easily seen where Marge is changing Bart and Lisa's clothes while they're walking downstairs.
Originally, the main story of Lisa being threatened by a female bully would have had Lisa try to punch Francine, but ends up punching Principal Skinner and gets sent to juvenile hall, sewing counterfeit jeans, but the writers rejected it. The premise of a Simpson kid getting sent to juvenile hall would later be seen in "The Wandering Juvie."
Lisa has a black eye for the first time after she was punched by Francine.
Nelson says no one will know the square root of a million, but the square root of 1,000,000 is 1,000.
Nails from a nail gun don't fly upon use (which was the same mistake seen in the first "Lethal Weapon" movie). They're released upon being pleased on an object. Also, Homer's nail wounds disappeared and he didn't bleed from being shot.
Looking at the footage of the pool, Francine had a nose-clip but in one angle, it's gone.
The Get-Well card business and Julius Hibbert must've forgotten that Homer didn't prevent childhood illnesses (or the fact that adults can get injured too -- and several past episodes reveal that Dr. Hibbert doesn't just treat children).