Continuity mistake: When the crew and Bender are sitting on the couch, Bender says, " Oh, oh, oh! get ready for this part!" Note the vent behind him is missing the three lights that have always been on it. (00:13:25)
Continuity mistake: Bender is shown to be wearing clogs in the scene where he arrives back from Holland after saving a turtle. However, a few seconds later when he's knocked over, the clogs are gone.
Continuity mistake: The lava is close to the machine, until Fry runs to it, then it's a long way away.
Continuity mistake: When Amy and Leela are wrestling, Amy's leotard changes several times. It varies between pink knee-length leggings and no leggings at all.
Continuity mistake: In the establishing shot of the science lab, Hermes' son is seen sitting next to a window made up of lots of panes. When he exclaims "My Manwich!", the window in the background is missing. (00:01:40)
Continuity mistake: People (even the dogs) flying through the asteroid belt wear space helmets, but on the asteroids themselves, they don't.
Continuity mistake: The back page that has been ripped off is put in the envelope with the top part showing the right way up, but it was folded so if the ads side of the page was showing, either the middle part or the top part upside down would show.
Continuity mistake: The rotation of the feeding mechanism on the newspaper gun changes. It first spins counter-clockwise when Hermes starts firing, then it is shown spinning clockwise for the shot where Dwight takes over.
Continuity mistake: The comic books pages become blank when Cubert is ripping off the back page.
Continuity mistake: In one of the first shots at the Freedom Day celebration in front of the Lincoln Memorial, we see a banner, with the text "Freedom Day - Express yourself. I hate my job.", suspended between to poles. Some of the banner can also be seen during the first part of Nixon's speech. But when it gets time to lower "Old Freebie" (the flag) the banner has disappeared and the flag is lowered into the position where the banner hung before. And the banner was tied to the two poles so they can't have raised it. (00:02:20 - 00:04:35)
Continuity mistake: On board the Nimbus where Zapp asks for the activation codes for the global defense network, it immediately after cuts to a shot of Kif Saying "Aye Aye sir". In the background of the shot sit two ship crew members, the brown haired one on the left disappears in the following shot. (00:13:50)
Continuity mistake: Just before Leela unhooks her bra, she drops her singlet on the floor. The singlet she drops is a pale orange colour, matching her bra, but Leela's singlet is white.
Kif Gets Knocked Up a Notch - S5-E5
Continuity mistake: Zoidberg wasn't in the machine to begin with, yet he appeared later. When it spins you see the whole inside of the machine - he's definitely not there.
Suggested correction: They even make a comment about this, he lives there. So he was probably sleeping under the grate but still got ejected. There's parts of the floor we don't see.
Kif Gets Knocked Up a Notch - S5-E5
Continuity mistake: When Zap Brannigan is about to shoot at the evil holograms the horse has fangs, but when they fly out the window the horse's fangs disappear.
Continuity mistake: When Leela is found on the door step she has a bracelet on her wrist but in the next shot it is gone.
Continuity mistake: When Fry (Captain Yesterday) is falling after the gem, the clock is at 10:05. When he lands and we see the clock, it's 10:35.
Teenage Mutant Leela's Hurdles - S5-E7
Continuity mistake: When the door is closed on the "ageing chamber," notice that the side the hinges are on changes between the external and internal shots.
Continuity mistake: When Fry, Leela, and Bender make it back to the ship, Fry's hair is messed up. When the bee is unfolding itself, Fry shouts "Look out!" and his hair isn't messed up. Then when he says the bee will have to go through him, his hair is messed up again.
The Farnsworth Paradox - S5-E10
Continuity mistake: In the very beginning scene, where Fry and Leela are talking, there is an explosion. When some ceiling falls down there is one big bit and three small bits next to Leela's foot but then a few seconds later there is one big bit and a few small bits all in different places. (00:00:40)
The Farnsworth Paradox - S5-E10
Continuity mistake: When Leela looks in the box, the wall behind her is red, then blue when it cuts back, then red again, and finally blue as she enters the other universe. (00:05:10)