Continuity mistake: When Bender laments that he'll be drifting through space with just a little swag, he takes a gold wristwatch out of the bag and puts it on. The watch disappears a few seconds later when he pulls the little piano out of his chest storage and is never seen again.
Continuity mistake: When Bender hits the asteroids, one pierces his head. Seconds later that asteroid is gone. Where did it go?
Continuity mistake: Near the end, when Leela talks to the second female blurnsball player, her black nose-stripe disappears then reappears throughout the shots.
Where No Fan Has Gone Before - S4-E12
Continuity mistake: When the Planet Express Ship first lands on the planet, it crashes with noticeable damage. When they try to sneakily escape while the screen play is going on (before they get the parts from the Star Trek ship), the damage is repaired.
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.