Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When Barnacle Boy opens the box with the two rings inside, in the closeup the "B" ring is on the left and the "M" ring on the right, but in the wideshot Barnacle Boy removes the ring on the left (the "B") and places it on Mermaid Man's finger, then in the next shot we see it's the "M" ring, before both rings vanish.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When SpongeBob and Patrick (dressed in their superhero costumes) exit the pineapple the front door opens at the right side (outward), but after getting on Squidward's nerves, when they retreat back inside the front door opens the opposite way at the left side (inward).
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 / Pickles - S1-E6
Other mistake: In the end credits for the episode "Pickles", Bubble Bass is named "BubbleBass" (without a space).
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.
Answer: I believe this is the Season 6 episode "Spongicus".