When Fry has a bite of his pizza slice, the pizza slice changes size between the shots.
When Bender's cans first fall onto the floor, they don't have labels on them, but in the next shot they do.
When Bender's cans first drop out of his jacket onto the floor, the number of extra items on the floor increases when the security cameras are looking down on him.
When Leela and Bender leave Fry's apartment the door opens from the left, but when Mom's three sons arrive the door now opens from the right.
When the crew is eating the pizza with anchovies, there are leftover anchovies in the tin sitting on the table. While everyone except Fry is gagging on the pizza, the fish in the tin disappear between shots, with no explanation.
Fray's still-standing bank account should be a savings account as checking accounts do not
accrue interest.
After Fry gets his money stolen by Mom's sons, he could have gone to the police or the bank and reported it.
It would have been easier to steal the anchovies from Fry.
Mom claims that robots need an oil change every 3,000 miles. But many robots on the show clearly do tasks that could not be measured in miles.