Homer states that he is now "the luckiest man on the face of the Earth now that Lou Gerhig is dead".
When the Simpsons are in the car, at one point Homer's head is misplaced slightly so that there appears to be a piece of shirt under the collar where his head is meant to be.
The tracks in the concrete appear before the railcar wheels rolled over it.
The idea of Grampa suffering a "kidney blowout" is medically impossible. His bladder would have been the organ that would have ruptured from holding urine in for too long, since the bladder is the organ that retains the urine before it gets expelled by urination (the kidneys just filter what the body has consumed).
As Dr. Hibbert laughs after Homer exits the hospital, the bottom of the knot on the back of his hat repeatedly disappears, so that there is a noticeable space between the bottom of the kot and Hibbert's shirt (even though the former is supposed to behind the latter).
Homer somehow manages to buy an outfit from Davey Jones' Hamper despite wearing his pocketless hospital robe and thus not possibly having his wallet with him.
In this episode, Grampa has two kidneys, but in Season 2 episode "Old Money", Grampa told Bea that he had one (unless he meant one that was still functioning). This also may be a mistake on Abe's part due to his senility.
When Homer signs the form in the hospital, he signs in the middle of the paper instead of on the line at the bottom. However, one could interpret this as simply an example of Homer's lack of intelligence and common sense.
When Homer was parallel-parking the railcar, he was out of proportion compared to the cars on either side of him. Oddly, he barely comes up to the height of the trunk on the closest car.
The Frenchman says he stole his accordion from a blind monkey, but what he's actually playing is a concertina. An accordion has a full keyboard on it, is boxy rather than circular, and wouldn't be held easily with two hands (accordions have straps on them worn on the body that keep it in place).
Homer is stated to still have both kidneys in later episodes, and when he is seen shirtless in "Alone Again, Natura-Diddily" and other later episodes, there is no kidney-shaped scar on his body. The scar probably healed after a while.