Waylon Smithers had braces and used to have brown hair in high 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 high school, and the kid he beat up would later be his boss's assistant.
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.
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.
If Homer beat up Smithers when he was a kid, shouldn't Smithers have recognized him when Homer applied for his job at the nuclear plant in "I Married Marge"? Homer didn't change all that much between the time he beat up Smithers and when he applied for the nuclear plant job in 1980 (except that Homer had a beard and his brown hair was slightly shorter).
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).