New Student Starfish / Clams - S3-E14
Continuity mistake: When SpongeBob and Patrick arrive to the class, SpongeBob writes Patrick's name in the board. Notice that he writes it in capital letters: "PATRICK". After, when Patrick is asked to say his name to the class, and he becomes nervous, look at the board, at Patrick's name: now isn't in capital letters, is normal: "Patrick".
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.
Your Shoe's Untied / Squid's Day Off - S2-E2
Continuity mistake: In Your Shoe's Untied, when Spongebob takes the patty to Squidward, it's just a patty with lettuce, but in one shot, you can see cheese and pickles on it.
Continuity mistake: In the morning when they all wonder where Santa is, and Spongebob keeps singing "Santa's coming tonight", once everybody walks away, Patrick appears right next to Spongebob.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: Spongebob, controlled by Plankton, wasn't aiming directly at Squidward's house, but he eventually breaks through the wall.
Your Shoe's Untied / Squid's Day Off - S2-E2
Continuity mistake: In Squid's Day Off, when all of the coins go out of the cash register, you see 14 coins drop. When Squidward picks up the coins, there are only 12.
Nasty Patty / The Idiot Box - S3-E4
Continuity mistake: When Mr. Krabs tells Spongebob to make sure the health inspector's head sticking isn't showing, Spongebob's shovel disappears.
The Bully / Just One Bite - S2-E17
Continuity mistake: In "The Bully" SpongeBob accidentally runs into Flats' dad's car and there is only one seat. Later Flats is shown sitting in the car.
SpongeBob's House Party (aka Party Pooper Pants) - S3-E10
Continuity mistake: When Spongebob comes home from the police station in the morning, he gets the spare key from under the mat. That mat definitely wasn't there last night.
Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: Before SpongeBob takes off his pants, his pants are the only thing that is hooked to the fish hook. Later in the scene, his underwear is hooked as well.
Pre-Hibernation Week / Life of Crime - S2-E13
Continuity mistake: When Spongebob has melted from stress and exhaustion, he is trying to talk and Sandy tells him to "hold that thought", and you can see the bike that they were riding, in the background. When she makes the fly fishing joke, the bike is gone, and there is a small plane. A few shots later the plane is gone as well.
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.
Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: In "Hooky," when Spongebob gets hooked, the hook changes from dark yellow, to dark pink, to dark blue in between shots.
Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: The track changes between days.
No Free Rides / I'm Your Biggest Fanatic - S2-E10
Continuity mistake: In "No Free Rides", after SpongeBob puts his socks on the boat he goes in the boat and falls asleep, yet when he is being dragged by the boat he has his socks back on.
You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Continuity mistake: When Gary goes through the pet door to run away from SpongeBob, when SpongeBob opens the door, there is no other side to the pet door.
The Bully / Just One Bite - S2-E17
Continuity mistake: When Flats moves out of the way we can see his pictures on the blackboard. The camera cuts away from him and back. The pictures are then taking up much more of the board than before (they go over the top of his head).
The Graveyard Shift / Krusty Love - S3-E13
Continuity mistake: When SpongeBob is cleaning the roof, you can see that there isn't nothing up there. The very next shot shows a closer view to SpongeBob and we can see that is a bucket there. That wasn't there before.
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.
Valentine's Day / The Paper - S1-E16
Continuity mistake: In "Valentine's Day", Patrick starts searching his present in the fair. Then he goes to a mountain and falls thinking that there will be his present. This mountain wasn't there before, even when they arrived to the fair.
Answer: I believe this is the Season 6 episode "Spongicus".