Continuity mistake: When Nudar says to Bender, "Go steal the Doomsday Device chained to the Professor's wrist", Nudar and Bender are around the same height. In the next shot, Bender is several inches smaller than Nudar. (00:27:55)
Continuity mistake: When Bender from the end goes back in time to put the code on Fry's butt he goes to put it on frozen Fry's butt. When Fry comes back in time, Bender from the end disappears. (00:37:20)
Continuity mistake: When Bender believes to have killed Fry in 2012, he is wearing glasses. In the next shot when he says "Whoo, I totally killed him", the glasses are on the ground without enough time to put them there. (00:44:00)
Continuity mistake: When Lars deactivates Santa's bomb, the bomb is stood up. However, when Fry says "I could make you happy too", the bomb is suddenly lying on the ground. (00:58:00)
Audio problem: At the Altar, just after Lars leaves Leela and she starts crying, her mouth doesn't open until way after she starts crying. (01:05:20)
Revealing mistake: When everyone is cheering to Bender, you can see Fry on the right hand side of the screen wave to him twice. The second time he cheers, his hands move from the table to suddenly waving at Bender without any animation. (01:19:50)
Other mistake: When Leela is signing the petition, Amy grows a third arm for a split second.
Continuity mistake: In the hybraxi, Al Gore's blazer is blue and he is wearing a red tie, but in the next shot, it is brown and he has no tie.
Plot hole: At the end, 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. There should have been only one Bender without the Obedience Virus, not all of them.
Other mistake: You can see in the church where Leela and Lars are getting married, someone in the audience's eyes jump off his face.
Other mistake: At the beginning of the scene involving the 2000 Presidential Election recount, a national election map is onscreen for a few seconds. Virginia is colored in Republican red, but the Eastern Shore of the state bordering Maryland is erroneously colored blue.
Other mistake: Fry got the tattoo while he was in the cryogenic device. Yet Fry has never had that tattoo until it was pointed out.
Suggested correction: No, but it's the same with many things in cartoons like this in that things don't roll over to following episodes or vice versa. Example. Kenny gets killed in most South Park episodes upto about S7. But he's always in the next episode.
Continuity mistake: When the Nibblonians attack the nudists, they fly out the window leaving smashes and one drives into the wall leaving a hole. The hole disappears when Nudar says he's going to do his test drive.
Continuity mistake: When Professor Farnsworth is typing in the bank account numbers, the buttons on the desk change color between shots.
Plot hole: When Nudar first uses the time sphere, he has to say "Yesterday" to go back in time. Yet whenever Bender goes back in time, he doesn't have to say anything.
Suggested correction: If you notice when Nudar was in the time sphere, time around the sphere seemed to slow down, so Bender could have just been faster than everyone else as he was stating the time he wanted to go to.
Audio problem: When Nibbler says "It's a paradox correcting time code. It all works perfectly", his mouth is out of sync.
Continuity mistake: When Bender asks Nudar where to put the auto dialer's, the computer on Nudar's desk keeps changing position between shots.
Deliberate mistake: Bender goes back in time to two minutes before Fry came back to the past. But if you time it, it was actually only 1 minute and 42 seconds.