Lisa's birthday was revealed in this episode. However, it is not exact. The date isn't mentioned, but it's the last day of the Olympics when Marge goes into labor. Therefore, it would be around August 24, 1983. Unless it was the Special Olympics of 1983, then her Birthday would be around July 18.
That second theory is completely disproved when Chief Wiggum says he could kiss Carl Lewis. Carl Lewis is not eligible for the Special Olympics.
This is one of many aging inconsistencies throughout the series' impressive run. When the series began in 1989, it was established that Bart was ten and Lisa was seven. That would put their birth years in 1979 and either 1981 or 1982 respectively. But it's a moot point since the characters' birthdates change as the series continues and because of that, Maggie has been a baby for 25 years as of 2014.
Lisa's first word was different from the episode "Lisa's Pony", when Homer is watching a video on tape when Lisa was a baby.
Bart's first words were also revealed in this episode: "¡Ay, Caramba!" He said that after seeing his parents having sex. This is a story Marge refused to bring up.
Bart's term of "Can't sleep, clown will eat me" was later used as a line in an Alice Cooper song. It has since become somewhat of a slang term to describe insomnia.
When Bart is packing his toys up he is saying something, but it's not audible.
The Krusty Burger scratch & win cards were inspired by a promotional game McDonald's did for the 1984 Olympics where an event would be revealed and prizes would be awarded dependent on whether Team USA scored a gold, silver, or bronze medal. Prizes ranged from free McDonald's food to a $10,000 cash prize. McDonald's lost millions of dollars paying out prizes on that promotion. Also like in real life, the reason for the loss of money was due to the Soviet boycott of the Olympics.
The footage of Homer building Bart's clown bed was recycled from him building his Wonderbat in "Homer at the Bat".
Whilst Marge is doing a flashback, some women mention the TV show M*A*S*H. One woman says she misses Klinger, a man who dressed as a lady to get out of the war, another woman says she loved Mike Farrell (B.J.).
This episode shows Lisa was very intelligent as a baby. This would be expanded on in the Season 9 episode "Lisa's Sax".
Shortly after Lisa's birth, Homer tells her that he has already started a college fund for her at Lincoln Savings and Loan [Association]. The Lincoln Savings and Loan Association was the financial institution at the heart of the Keating Five scandal during the 1980s savings and loan crisis. When American Continental Corporation, the parent of Lincoln Savings, went bankrupt in 1989, more than 21,000 investors lost their savings.
Sideshow Bob was shown with blue hair in this episode.
Even though it is obvious Grandpa is a younger man in 1983, a picture of his elderly self hangs in the wall of his house.
The unicycling jugglers in the couch gag wear orange shirts when they first appear, but when they go into the background, they are wearing green shirts.
Why didn't Bart just eat Lisa's lollipop? It is possible that Homer ate it.
In the Season 1 episode "Krusty Gets Busted," Krusty says he is (and always has been) illiterate. In this episode, however, Krusty can read a wire communique about the Soviet boycott. (He could be functionally illiterate, in that he can read something, but not know the deeper meaning of what's being read, but "Krusty Gets Busted" makes it clear that Krusty is a garden-variety illiterate).
Sideshow Bob is in this episode, but he has turquoise colored hair.
Todd Flanders is the same age as Lisa (8) and yet in this episode he is approximately the same age as Bart (2 in the episode, 10 in modern day). In fact, Marge is still pregnant with Lisa making a talking Todd impossible. Even accounting for the error of misnaming Rod (12), it's still an age error since Rod is 2 years Bart's senior.
Despite calling her dad Homer like Bart in this episode, Lisa does call him Dad in other episodes.
In Boy Meets Curl, Lisa says she won the pearl necklace when she could first read at the fifth grade level, but in this episode, she already have the pearls when she was a baby.