In the scene where Flanders is at Burns' Mansion trying to pitch recycling Burns states, before releasing the hounds, "I see you have your running shoes on. That's a good thing." You can see here that Flanders is wearing his Assassin shoes from Bart's Dog Gets an F.
When the family is posting up lost signs for Santa's Little Helper, they are shown putting one on a pole over the one of Principal Skinner's "Have you seen my body today?" signs from Bart the Murderer.
The pictures of Santa's Little Helper the family has that Marge doesn't like are: Homer kicking Santa's Little Helper, Homer strangling Santa's Little Helper, Santa's Little Helper biting Homer's arm, Santa's Little Helper burying Homer in the yard, and Santa's Little Helper knocking Homer out like a heavyweight boxer. The one the family uses for the "Missing" posters shows a frightened Santa's Little Helper about to be strangled by Homer.
The scene where Santa's Little Helper is brainwashed (by having his eyes pinned open and watching footage) is a parody of the rehabilitation process of Alex DeLarge in Stanley Kubrick's A Clockwork Orange.
When leaving the vet for the first time after finding out Santa's Little Helper is sick and the family is in the car. It shows they are in Marge's station wagon since Bart and the dog are in the cargo area and the car is red. But when the camera changes to show the car going down the highway the car looks like Homer's sedan and it is also pink like his car.
In this episode Santa's Little Helper saves a baby from a burning house, fights a bear and defends Bart from hounds. However, in Old Yeller-Belly, he is depicted as a coward. He could have gradually become more cowardly over the years.