Put Your Head on My Shoulder - S2-E10
Continuity mistake: After the accident when Fry looks at his body, there is a tool kit or something similar more or less right in between the body's legs. In a few moments there is a shot from above and the kit is several feet to the right of the body without anyone touching it.
Anthology of Interest 2 - S4-E3
Continuity mistake: When Bender is strapped to the table at the beginning of the reverse fossilization process, he has sensors on his sides, ears and ankles. During the process he magically gains alligator clips on his fingers and toes and sensors on his wrists. They spontaneously appear when the Professor pulls down the lever to start the process.
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)
Continuity mistake: When Leela is feeding Nibbler there are two drawers and two knobs right behind Nibbler. When it cuts their positions and appearance change. (00:00:55)
My Problem With Popplers (a.k.a. The Problem With Popplers) - S2-E18
Continuity mistake: When the hippie tells everyone to join hands, the cord from the microphone change position in the next shot. (00:19:10)
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)
That's Lobstertainment! - S3-E8
Continuity mistake: The patches on Uncle Zoid's jacket sleeves appear, disappear and change from left sleeve to the right during his conversation with Zoidberg in the restaurant.
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)
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.
Anthology of Interest I - S2-E20
Continuity mistake: When giant Bender falls backwards over the building and gets impaled by the spear, the spear's design changes between the shots. (00:06:00)
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.
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: 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.
Continuity mistake: After destroying the toy spaceship Bender place the hammer on the ground in front of him. When it cuts the hammer has changed position. (00:00:55)
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.
I, Roommate - S1-E3
Continuity mistake: When the team are gathered round the table at the beginning of the episode, note their positions when the video screen is turned on. When they see Fry drying his hair, Leela and Bender have each moved up a chair, and Zoidberg has also moved, and seems to have taken half of his previous chair with him. (00:01:20)
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)