Revealing mistakes: As Farnsworth enters his account information, the numbers he reads are already visible (albeit faintly).
Miscellaneous: In the scene with Amy, Nibbler, Leela and the nudist alien scammers at the Nude Beach Planet, Amy is accidentally drawn with a third arm.
Revealing mistakes: At 1 hour & 3 minutes in, during Lars & Leela's wedding, a man standing at the very back of the church has his eyes jump from being perfectly on his face, to having one eye on and another floating in mid-air. Obviously, the Korean animators goofed a little in photography, and the slides for that scene had the man's eyes just off mark.
Continuity: In the wedding scene, the robot police officer is seen in the crowd with pink for his helmet and yellow for his visor, but after cutting away and back to the scene, his helmet have returned to their normal colors.
Incorrectly regarded as goofs: The Nobel peace price is presented in Oslo, not in Stockholm as the movie depicts. Since the time stamp on that particular presentation is 2308, however, there's sufficient time for the Nobel Organization to move the location. Also, there were no contextual clues to point to Stockholm being the location presented.
Incorrectly regarded as goofs: Only the male of the Narwhal whale species has a tusk. Leelu is a female. However, it is a very rare case when female Narwhals have tusks, which was referenced in the movie as Leelu being a "rare horned female narwhal."
Incorrectly regarded as goofs: In "The Devil's Hands Are Idle Playthings," after Bender made a deal with the Robot Devil and deafened Leela, Leela made a deal with the devil to restore her hearing, which he did with Calculon's ears. In Bender's Big Score, however, she has recovered her hearing and has no robotic ears. However, it has been at least two years from "The Devil's Hands are Idle Playthings," making it entirely probable that she could have received enough treatment to no longer need the robotic ears.
Incorrectly regarded as goofs: None of the duplicate Benders that are waiting in the limestone cavern under the Planet Express building have had their Obedience Virus or the time code deleted from them. Yet there was one Bender that did, and it is entirely possible that, when he went down there the last time, he was able to present all of the other Benders with the anti-virus. This makes sense when he states that he convinced them to come up at a different time than they should have, making it entirely possible for none of them to now have the virus.