When Fry and Bender are in the museum and locked in the "Villains" room, Bender breaks the two girders in the window, and then his arms falls off. As he puts his arms back in, you can see behind him that the girders are back in place in the window.
When the team are gathered round the table at the beginning of the episode, note their positions when the video screen is turned on. When they see Fry drying his hair, Leela and Bender have each moved up a chair, and Zoidberg has also moved, and seems to have taken half of his previous chair with him.
When the spaceman is delivering the 'Planet Express' package, the colour of the rocket on the box changes from black to green. The same thing happens to the spaceman when he's picked up by the large bird - the logo on his backpack changes colour.
When Fry, Leela and Bender are in the mutant village they walk past a building which has the sign on it "Dry Cleaners." However, when the shot cuts to the close up, it has suddenly changes to just "Cleaners."
When Fry is watching "All My Circuits" for the first time, it shows Calculon screwing a golden bolt onto the index finger of a fembot's right hand. In the very next shot, the bolt is on the middle finger of her hand.