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.
Revealing mistake: In the scene near the beginning where Leela tells Fry and Bender to watch the political debate on television, both of them (Fry and Bender) fall asleep. When Leela "hops" on the couch to wake them up, Bender's arm, despite being behind Leela, can be seen through her white shirt for a few frames.