When Homer gets on the scales and could see the dial (225 lbs), Bart points out that his belly is caught on the towel rack in front of him. So how did Homer manage to see the dial?
Right before Homer goes out to the movies, Bart and Lisa come home from school. In a later scene after Homer stole an ice cream truck, Lisa is on a school bus talking to Ralph, presumably on her way home.
At the ending during the award ceremony for Homer, Marge is seen in the long shots wearing lipstick. In her close-up the lipstick is missing.
When Mr. Burns is announcing Homer to work at home in the Simpsons' house, he is standing by the back door, but after Homer says "thank you for your pity", Mr. Burns disappears and instead Marge and Lisa are at the back door. In the shot immediately after, Mr Burns reappears there and Marge and Lisa are nowhere to be seen.
The Japanese dunking bird that Homer uses to type the "Y" key on his computer keyboard would stop moving very quickly, because it must dip its beak in water to cool the fluid that powers the motion.
When Maggie hands Homer a 'doughnut' while he's standing on the bathroom scales, the dial displays an immediate increase in his weight of one pound (before the 'towel rack'). He would not have to eat the doughnut to achieve the result.
Several of the hardships Homer encounters seem to be there merely for the plot convenience. Homer's fingers would likely not be too big to dial a phone, and he could use a pencil or any similar slim device to dial numbers. The stress of Homer, a 300+ lb. person, entering a car would not cause four simultaneous tire blowouts. That car routinely hosts the full family, whose combined weight exceeds 300lbs, with no blowouts.
Homer blames 'lousy farmers' for Daylight Savings days. Farmers are actually more likely to be opposed to DST, as it means fewer daylight hours in the early morning, which is when most of them start work.
During Homer's fantasy of being fat, Ned is seen coming home and when Homer's asked him about his day Ned says that "Yeah, a crazy guy shot a bunch of people and the subway ran over my hat." This indicates he has an office job but in reality he runs The Leftorium.