The Bully / Just One Bite - S2-E17
Audio problem: In "Just One Bite", Squidward is running, then tiptoeing by Spongebob's house. The sound of his running is fine, but the sound of tiptoeing is faster and not in sync with with movement.
Dying For Pie / Imitation Krabs - S2-E6
Continuity mistake: SpongeBob makes Squidward a tear jumper and there is a shot of Squidward sighing. In this shot, we can see no-one standing around the register. In the next shot, Mr. Krabs has suddenly appeared next to it.
The Secret Box / Band Geeks - S2-E14
Continuity mistake: When the band is marching through the streets, whilst Squidward is pressuring the flag twirlers to move faster, there are some fish drumming behind them. One is a blue fish wearing a yellow shirt seen standing on the left, and another is a brown fish wearing a red shirt seen standing on the right. When the flag twirlers behind to fly off the ground, those two fish have swapped places.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Revealing mistake: When we see Billy get told about the stupid squirrel, he has a sleeve going through his arm. The moment he starts talking, the sleeve disappears and his arm extends over his shirt. Around the end of the shot when he's being pulled away, the sleeve returns.
Continuity mistake: In "Jellyfishing" when Squidward gets home from the hospital, Patrick exclaims Merry Christmas! However, later on in the series it is revealed that nobody in Bikini Bottom even knew what Christmas was.
Suggested correction: The episodes are not always meant to be in chronological order. It's entirely possible that "Christmas Who?" took place before "Jellyfishing."
The Bully / Just One Bite - S2-E17
Continuity mistake: In the episode "The Bully," when Flats punches Spongebob, Spongebob states to Gary that he's made out of some spongy material, that it absorbs his blows and it doesn't hurt him at all. But in later episodes, when Spongebob gets knocked out that never happens anymore.
Procrastination / I'm With Stupid - S2-E19
Continuity mistake: Procrastination: When Gary eats all the food, he burps out his bowl. A ladder suddenly appears next to it.
Big Pink Loser / Bubble Buddy - S2-E3
Revealing mistake: Big Pink Loser: When Patrick is answering phone calls, the third time he picks up and says, "No, this is Patrick", the anchor symbol on his hat briefly vanishes. (00:04:36)
Suggested correction: This mistake can only be detected by freezing the film and advancing frame by frame. It is not visible while watching the film at a normal running speed. According to the rules of this site, this invalidates the error.
So, I reworded the mistake to say that it "briefly vanishes," because it's actually gone for a few frames, not one. I did not advance frame by frame to find the error. If you watch the scene at normal speed, it disappears for a brief moment, then comes back. I assume this correction might have been made without watching the scene, especially since the show was referred to as a "film."
This is not true. You can see it disappear if you watch it at normal speed; it does not require pausing at all. At least, I am able to see it.