Homer quotes Friedrich Nietzsche when saying "Whatever doesn't kill me can only make me stronger!" This reference is reused in the Season 16 episode The Heartbroke Kid when an obese Bart says "Whatever can't kill me only makes me stronger!", where he also gets a heart attack.
When the X-ray of Homer's heart being taxed by Mr. Burns' stress is shown, during the heart attack the four suits of cards (♣,♠,♦,♥) is shown.
In this episode Sideshow Mel is shot inside a cannon just like Sideshow Bob in Krusty Gets Busted.
Some of the people in the hospital when Homer arrives are: Groundskeeper Willie with arm casts, Jacques with his finger stuck in a bowling ball, Jasper Beardly with his beard stuck between the spokes of a bike, Apu with a bullet wound, Akira with his hand stuck on a wooden board, Sideshow Mel stuck in a cannon and Chef Wiggum with a locked jaw.
During Cops from Springfield Chief Wiggum breaks the fourth wall saying the man who jumped out of the building and he tried to surrendered to him is crazy. This is not quite breaking the fourth wall, because it is featured as part of a television show within the world of the Simpsons. Though Wiggum is acknowledging an audience (the viewers of "Cops: Springfield"), the actual "fourth wall" of the Simpsons universe is never broken
During the "Bad Cops" section in the start of the episode, the cops are looking for someone living at 742 Evergreen Terrace, which is where the Simpsons family lives (though this episode was part of the early ones in which the Simpsons' address was 1094 Evergreen Terrace).
In one scene were Homer is eating his bacon and eggs, they change color between shots.
Homer had to pay for his operations, but when it comes to life-saving operations, like Homer's bypass surgery, the operation will become free.
Lisa gives Dr. Nick instructions on how to perform the bypass surgery, but she gave the instructions while in the medical amphitheatre. The windows of a medical amphitheatre are soundproof.
Homer comments to Dr. Hibbert that $40,000 is too expensive and that he ought to just acquire a defibrillator. Owning a defibrillator actually would be more expensive than the $40,000 Dr. Hibbert requests to perform the surgery. In later episodes, Homer is shown with a defibrillator in his house.(They are now about $1500 for an in-home AED/defibrillator)
Krusty claims that his face was permanently blanched by his heart attack. However, in the 1990 episode "Krusty Gets Busted", he is shown with a flesh-colored face in the courtroom, and in "Brush with Greatness", Krusty could easily wipe off the clown make-up on his face.
Connections to future episodes
Homer seems to have entirely forgotten about the surgery in Bart Carny. When Marge warns Homer he cannot go on a ride due to his quadruple bypass and nearly died, Homer brushes it off, only to complain of his heart when on the ride.
In a later episode, Marge mentions that Bart and Lisa helped Dr. Nick perform heart surgery, referencing this episode, yet Bart did not do anything, and Lisa only pointed out to Nick where to make the incision.