Big Pink Loser / Bubble Buddy - S2-E3
Revealing mistake: Big Pink Loser: When Patrick says, "Why can't I do anything right?", and starts hitting his broom on the floor, the drinks that are supposed to be on the customers' tables are instead layered behind them. (00:05:18)
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: Bubble Buddy: When Spongebob brings his Bubble Buddy to the Krusty Krab, Squidward's restaurant hat is visible on his head. It is not seen when he looks into Bubble Buddy when he says, "That Bubble Buddy sure looks good."
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: It seems to me that half the cards that Spongebob used for the card snail have disappeared when Patrick comes in.
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: When Patrick in Spongebob clothing is first revealed (when the rock is raised), Patrick has no collar, yet in other shots the shirt has a collar.
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: At the beginning of "Big Pink Loser", Patrick's rock is brown. When Spongebob and Patrick run with each other, out of the Krusty Krab, Spongebob runs into Patrick's rock, painted like Spongebob's pineapple house, yet when Patrick said "I'm going to defend my title" or something like that, the rock is brown. The rock can't possibly paint itself.
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: The broom that Patrick throws on the ground in Big Pink Loser disappears soon after.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes", on Spongebob's second act when Sandy laughs about the bronze fish, she is between 2 people. When you see her again she isn't between anybody.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In Squirrel Jokes, when Spongebob comes out for his second act, there's a back shot of a crowd, and there is one guy in the front right (from the back view) who is green. There is another front shot of the crowd and the guy completely disappears.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes", SpongeBob wants to make a joke about a fork. Someone screams "Forks?" and SpongeBob becomes more nervous. After that, the fork disappears from where it was.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes", right when he comes out of the curtains people put their hands up, but in a front view their hands are down.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes", when Spongebob tells the joke about Squirrel in the second act she's at a table alone, but in the next wider shot there's a chair next to her.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes", at the beginning of Spongebob's 2nd act when he's at his mirror backstage, a random object appears on the table.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In Squirrel Jokes, when Spongebob gives Sandy the flowers, the number of the flowers varies from 6 to 8 in different shots.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: During Spongebob's act, he says to the audience, ".I'd like to give a special thanks to my friend Sandy over here" and the spotlight moves from Spongebob to Sandy. A few shots later, when Spongebob is talking to Sandy, the spotlight is suddenly no longer on Sandy. Then when Spongebob yells "Am I right?" to the audience, the spotlight is on him and as he turns to talk to Sandy again, the spotlight is altogether gone; it's not on either one of them.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: When Patrick is struggling to carry a heavy box, he drops it a number of times on Man-ray's foot. The camera cuts away, then back to Patrick and Man-ray, and the box has disappeared.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: In "Squirrel Jokes" when Spongebob drops his mic on the stage and he goes behind the curtain, the mic disappears soon afterward.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Audio problem: In "Squirrel Jokes" when Sandy is in the Bargn'-Mart and she can't decide which deodorant she wants, a fish says, "Maybe she should get both." His mouth says something else.
Mermaid Man and Barnacle Boy III / Squirrel Jokes - S2-E4
Continuity mistake: Before he comes on his second act, there is a front shot of the crowd, you see a guy in the front with his hands up, but in the next shot, which is of his back, his hands are down.
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: When everybody comes to Squidward's house to persuade him to write a letter, you see that all the paper and pencils and bottles on the ground disappear.
Answer: I believe this is the Season 6 episode "Spongicus".