Marge's reaction when Homer proclaims that it was Santa's Little Helper who buried all of their stuff implies that she herself was responsible for burying at least one of the items in the back yard—most likely, Homer's "The Best of Ray Stevens featuring the Streak" album.
This is the second time Bart uses a swear word, in this case 'Bitch', it's proper context, but still gets told off for saying it.
"See My Vest" follows the same tempo as the song it is parodying.
The episode title and plot are based on the Disney film 101 Dalmatians; Burns' plan to kill the puppies and turn them into clothing references Cruella de Vil from 101 Dalmatians, who wants to do the same thing. In addition, the maid who briefly appears during "See My Vest" looks like Nanny from the movie.
Bart and Lisa's rescue of the Puppies is based on the actions Sergeant Tibbs and the Colonel from 101 Dalmatians.
Smithers helping Mr. Burns steal the puppies is based on Horace and Jasper.
The scene where all the puppies are standing up is a parody of "I am Spartacus" from Spartacus.
Santa's Little Helper and She's the Fastest got together as a dog couple similar to Lady and the Tramp and had puppies just like Pongo and Perdita.
Homer and Marge had Santa's Little Helper and She's the Fastest like Jim and Darling, but when they saw that the puppies are born, they become like Roger and Anita Radcliff.
The Simpsons have 25 puppies, but there are 26 puppies while they are eating.
Bart is barefoot after Lisa takes his shoes and socks off but after getting cornered by Mr. Burns and Smithers Bart is now wearing his shoes.
At the scene in the pet shop, the animation of Santa's Little Helper is very choppy. Several times, his head cuts from looking forward to looking to the left without any in-between frames.
When the Simpsons are watching the dog race, there are a few frames where the bottom left curl of Marge's hair is incorrectly drawn and colored as if it was part of her head.
When the puppies are eating in their dog bowls, they are seen in a far away shot scattered throughout the kitchen. However, when the camera pans to showcase all the dog bowls, they are in a straight line.