Continuity mistake: When Bender is brought into the surgery tent and Zap is holding Nixon, the level of the fluid in Nixon's jar changes between angles. In the wider shots it covers his whole head, in the closer ones the top of his head is above the fluid.
Continuity mistake: After the fight with Destructor when Bender lies flatten to the ground, the wrestling manager appears with nothing in his hands. When it cuts he is suddenly holding a cigar.
Continuity mistake: At the end of the episode, when Bender and the Countess Delaroca are hanging on to the escape pod, the diamond on the diamond bracelet the Countess was hanging onto changes position between shots.
The Honking - S3-E1
Continuity mistake: When we see Bender welded to the wall the paintings on his sides are both hanging about a feet away from his arms. When he gets off the wall it's obvious the paintings have moved much closer to him. (00:11:55)
Continuity mistake: The lava is close to the machine, until Fry runs to it, then it's a long way away.
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.
Continuity mistake: In the intro, before the main titles, the Professor informs the crew that he's booked them on the maiden voyage of the Titanic. When Leela says "Looks nice," at the beginning of the "scary" Titanic montage, the right side of her shirt is undamaged. During the middle of the "scary" Titanic montage, it suddenly becomes torn.
Continuity mistake: When Fry and Leela dig out Santa there are cracks in the ice around him which disappear when they lift him up.
Xmas Story - S2-E8
Continuity mistake: When Bender goes off the cliff, we see in the overhead shot that there are no kids on the icy lake, nor are there any tress near the lake. When it cuts there are kids on the ice and trees surrounding it. (00:02:45)
The Honking - S3-E1
Continuity mistake: When the attorney reads up the will to the butler the attorney has no paper under his arm. When it cuts papers appear under his arm. (00:03:05)
Put Your Head on My Shoulder - S2-E10
Continuity mistake: When the tow truck appears to tow Amy's car back to Earth, the window is completely steamed. The tow truck driver only wipes away a small bit of the steam but in the next scene the window is completely clean.
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.
Episode Two: The Series Has Landed - S1-E2
Continuity mistake: When the spaceman is delivering the 'Planet Express' package, the colour of the rocket on the box changes from black to green. The same thing happens to the spaceman when he's picked up by the large bird - the logo on his backpack changes colour. (00:00:30)
The Honking - S3-E1
Continuity mistake: When Bender wakes up in the transmission fluid the fluid's appearance change between the shots. (00:09:05)
Continuity mistake: In the clip before Fry knocks Fox off the air, the one person says, "Could you repeat the last part? *pause, cut.*" When we later see it broadcast on Omicron Persi 8, it says, "Could you repeat that last, *cut*."
Continuity mistake: When Dr. Zoidberg walks out of the bathroom, he zips up his shirt, and the zipper is just visible above his buttoned up jacket.After that, it's not seen in this episode or ever again. (00:01:45)
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.
Episode Two: The Series Has Landed - S1-E2
Continuity mistake: When Fry and Leela are walking on the planet's surface, they have shadows. When they are next seen, the shadows have disappeared. The shadow inconsistencies happen again later when the buggy's wheel falls off and they try to outrun nightfall. (00:13:55)
Continuity mistake: The comic books pages become blank when Cubert is ripping off the back page.
A Big Piece of Garbage - S1-E8
Continuity mistake: Most of the objects on the Mayor's desk disappear (e.g. the photograph, the lamp) when Professor Farnsworth starts to write his plan on it. (00:17:10)