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.
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)
The Crest of Sincerity - S1-E17
Continuity mistake: In the scene where the DigiDestined are running towards a cactus mirage, Patamon is visible instead of Tokomon. (00:03:20)