Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Plankton! When Plankton pulls out a radio player to play his evil music on SpongeBobs pillow, it has disappeared when Spongebob wakes up. SpongeBob didn't move on it.
Continuity mistake: After getting the uranium, Stewie places it in the time pad and then puts the pad in his jacket pocket. After being confronted by Hitler who promises to spare them if they sing a musical number, Mort interrupts them, and it's seen that he is now standing on the time pad.
Heads Of Beef / Klub Katz - S1-E11
Continuity mistake: In "Klub Katz" Courage spins his head once or twice. But when he puts his head back on it spins way over once or twice. (Like a thousand)
Happy Birthday, Kevin (or Happy Birthday, Douchebag) - S1-E12
Continuity mistake: After Carlos sees the snake on the pole he leaps off the roof onto the pole. When he jumps you can see it's quite a distance from the roof. After catching the snake he is holding onto the pole and asks to be helped back onto the roof. The other characters just put their hands out and pull him up. There was no way with the distance between the pole and the roof they could have come close to reaching him the way they did.
How The Elephant Got Its Trunk - S3-E6
Continuity mistake: Papa Lazarou's black/brown and white face is supposed to be his real skin, however it is very different to his photograph.
Suggested correction: Do you mean the photo of the real Keith Drop when they are in the house with Brian and the lady from the charity shop? If so that person is not supposed to look like Papa Lazarou with black/brown/white face as it's in fact a photo of the person he is impersonating and whose identity he has stolen, e.g Keith Drop when who has the appearance of a white man, hence why Papa is painting his face with make up to look like him.
Laugh, Ed, Laugh/It's Way Ed - S1-E10
Continuity mistake: In "Laugh, Ed, Laugh", when Eddy is gambling with squirrels, he picks up a bunch of nuts, primarily acorns and only a couple of peanuts. But next shot later when he yells, "Suckers!", there are more peanuts shown. (00:05:00 - 00:11:15)
Continuity mistake: When Tim and Mike are paintballing, they meet a man who says he is a businessman. As the businessman stands up, he gets shot by Duane Benzie with a yellow paintball. Watch closely as the businessman's jacket is blown open by the paintball impact, and then manages to become buttoned up again.
Continuity mistake: In the scene near the beginning when Tom and Linda are talking to Jez and Suze, Tom invites them round for dinner, and says he will cook a spinach pie. He is leaning against the door frame with his right arm up as Suze agrees, but then there is a change of camera shot, and Tom's arm is suddenly down at his side, and not touching the door frame at all. (00:03:50)