Ralph's teasing about Homer and a restaurant could be a reference to what he actually did do as said in 'New Kid on the Block' when he ate for hours on end at 'The Frying Dutchman' until they eventually kicked him out.
The cover of the book "Am I Disabled?" depicts a picture of a man with a rod through his head. This references Phineas Gage, a man who experienced a large iron rod going through his head and subsequently suffered from significant brain damage.
When Homer is at the movie theater, someone (possibly Raphael, the Sarcastic Middle-Aged Clerk) suggests the movie "A Fridge Too Far", a joke of the WWII film title "A Bridge Too Far".
The song "Push out the jive, bring in the love" by the Lostprophets most likely takes its name from the phrase used by Mr. Burns during exercise.
Marge breaks the fourth wall saying, "But this season...", probably referencing the season that the episode is on. That's the joke. Marge was probably referring to a season like Fall or Spring, but to the viewer it sounds like Marge is breaking the 4th wall.
The name of The Vast Waistband (the store Homer visits to buy a muumuu) is a pun on the pop-culture phrase "vast wasteland," which was used in the 1960s to describe how American television programs were devoid of quality programming.
When Homer hits "TAB" thinking he'd get a drink while looking for the 'Any key', a startup sound from a Macintosh computer produced in 1995 is heard. This episode aired the same year.
When Homer vented the toxic gas from the plant, thus ruining the farmers' corn crop, the farmer says "Paul Newman's gunna have ma' legs broke!" when lamenting the loss of the corn (though the closed captions replaced "Paul Newman" with "Jollytime"). This is a reference to the legend made by the Newman's Own Popcorn company where Newman threatened people if they try to steal his popcorn recipe.
A sign on Homer's car-stop reads "Give me a ride or everybody dies!"
In Bart's fantasy he washes himself with a rag on a stick similar to a man who appeared on the news a few years before this episode.
Mr. Burns pays for Homer to get liposuction in the end of the episode but he ends up being 239 pounds again instead of a healthier weight. However, it could be possible that Homer still continued his unhealthy eating habits, returning him back to his overweight self.
Ralph pokes fun at Lisa for her dad being overweight, although his dad is also overweight.