RoboCop — The "Cyborganizer" show Homer watches is a spoof of the 1980s science fiction-police movie.
Shirley Temple — Former child actress Lil' Vicki Valentine is based on Temple. However, Shirley Temple went into a different line of work as an adult, having become a U.S. Ambassador. She often used the name Mrs. Charles Black (after her husband) to gain credibility in her adult life and not be solely associated with a child actress.
The Red Shoes ---- Lisa's self-tapping shoes wouldn't stop controlling her feet, similarly to how the red shoes forced a girl named Karen to dance endlessly. The Red Shoes is a story written by Hans Christian Andersen.
Ralph is usually very clumsy, but he can tap-dance very well in this episode.
Homer apparently can't tell the difference between Marge's voice and someone impersonating her (cf. the scene of Homer being kidnapped and tricked into buying Jack Daniels and cigarettes for Dolph, Jimbo, and Kearney). And it never shows nor explains how Homer's eyes go back to normal.
So far, this episode is first with a visual variation of the Gracie Films logo, where after the "Shhh!" we hear Little Miss Vicki saying "Tappa, tappa, tappa" and then the logo's main animation slides up to take up the top half of the screen, while the bottom half has an animated black-and-white scene of a cat rubbing its eyes (with fake prop arms from offscreen) and smiling (this was in an old Miss Vicki movie Lisa was watching). Another one would later appear 17 seasons later with Looking for Mr. Goodbart in Season 28.
Why would Kearney need Homer to buy Jack Daniels and cigarettes for him when Kearney is of age to get it himself (unless Kearney was setting Homer up for the crime of buying beer and cigarettes for minors [i.e. Dolph and Jimbo])?
When Homer is unknowingly in the car with Kearney, Dolph and Jimbo, Jimbo's hat is gold instead of its normal color, purple.
This episode takes place in February (just before the Presidents' Day weekend), and yet Bart and Milhouse plan on going to camp for a week. It may be spring break week camp.
When Bart and Milhouse sees the Puma in the bushes Milhouse is barefoot. During the chase he is now wearing his shoes.
After the puma plays with the first ball of yarn, its eyes are white.
It is never explained what happened to Bart and Milhouse after the puma ate the ball.