Continuity mistake: When Bender is brought into the surgery tent and Zap is holding Nixon, the level of the fluid in Nixon's jar changes between angles. In the wider shots it covers his whole head, in the closer ones the top of his head is above the fluid.
Add timeDavid Mercier
Continuity mistake: When the robot at the start is dying, the doctor opens a panel to see his "heart beat." After a couple of other shots we see the panel again and this time it's closed without anyone touching it. It's also important not to confuse the doctor closing the robots eyes with this panel.
Continuity mistake: When Fry, Leela and Bender enter the orphanarium you can see 3 owls. In the next shot you can see 1 owl walk down the corridor. In this shot you can also see the door and no owls go through there, but in the next shot the other 2 have disappeared.
Add timeMatty W
Revealing mistake: In the final battle, Bender has fry trapped into the seat inside of him, and he drives over a ramp and nearly smashes into the original were-car mid-air. But when the were-car lands on the same ramp that Bender took off from, we see that the furnace is literally touching the end of the ramp. How did Bender get up enough speed to launch himself into the air, especially accidentally (he would have had to turn 90 degrees to get onto the ramp) with the furnace that close? Also at the start of this scene, we see the were-car crying in front of the furnace, and the ramp is nowhere to be seen.