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. (00:19:50)
Continuity mistake: In the episode "Mars University" we are shown how robots in "Futurama" attend a regular college, alongside humans and other species, over a periode of at least one college semester. Bender even talks about how he attended and majored in bending (minoring in Robo-American history). However, in this episode, we are shown that his entire "education" consisted of downloading a file at the factory where he was made. There is a clear inconsistency in these two stories of Bender's education.
Continuity mistake: When they find Bender on the ground after being hit by the were-car Fry asks if any of them have any liquor you see all of them reaching out a bottle of liquor. When Bender grabs one of the bottles it cuts and you see all of them standing back as if none of them were handing him anything. (00:06:25)
Continuity mistake: In the scene where Leela and the doctor are driving out of town and throughout the episode Leela's second eye is following her motion. This despite the fact that in a previous scene we could see that she was unable to move her second eye. (00:09:55 - 00:12:00)
Continuity mistake: The way Professor Farnsworth holds Leela's jacket changes as he goes to give it to Fry and then Bender. He's holding it from the back at first, but in some shots he's holding it from the front. It changes in Bender's hands too from back to front.
Continuity mistake: When Nibbler bites the balloon and goes flying up, you can see there's a big open space between the "cream" booth and the "soylent chow" booth. And there's no curtain partition behind the booths. When he lands, the booths are right next to each other and you see the curtain.
Continuity mistake: When Fry and the kid are racing along the motorway, just after they let go of the cars they are holding onto, they head into a lamp post. This leads them to banging their heads and collapsing on the floor, because the ribbon they were holding onto forces them into the lamp post. When they fall on the floor, the dust shoots up. After the dust disappears, the lamp post has as well, meaning that the ribbon isn't actually tied around anything.