Bummer Vacation/Wigstruck - S4-E14
Continuity mistake: In Wig Struck, Patrick takes a bite out of Spongebob's wig and in the next shot, the wig is restored.
Continuity mistake: SpongeBob is holding a picture of Plankton and Mr. Krabs, then when he pulls Plankton and Mr. Krabs together, the picture disappears.
House Fancy/Krabby Road - S6-E1
Continuity mistake: In House Fancy, Squidward gets a bad sofa injury. In the next shot, his feet seem fine.
Continuity mistake: Throughout the whole episode of "Missing Identity", SpongeBob's shirt is backwards. This is seen with his sleeves being supposedly behind him. The sleeves are missing from the front, which is normal, but throughout the episode, pay attention to behind SpongeBob. His sleeves are supposed to be behind him, but are missing altogether.
No Weenies Allowed / Squilliam Returns - S3-E6
Continuity mistake: At the beginning of "Squilliam Returns," Squilliam is walking to Squidward from the left of the garbage pails. When Squidward throws his hat out, Squilliam is to the right of the garbage pails.
No Weenies Allowed / Squilliam Returns - S3-E6
Continuity mistake: In "No Weenies Allowed," when Spongebob gets punched by Patrick, he doesn't have a black eye. When the shot zooms to Spongebob's face, he has a black eye.
Big Pink Loser / Bubble Buddy - S2-E3
Continuity mistake: The broom that Patrick throws on the ground in Big Pink Loser disappears soon after.
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: When Spongebob is cutting his Jack-O-Lantern, he cuts out an eye on his right, but in the shot from inside the pumpkin the eye hole is gone, then the eye reappears.
Patrick SmartPants/SquidBob TentaclePants - S4-E8
Continuity mistake: SquidBob TentaclePants: When the mixed-up SpongeBob and Squidward come out of Sandy's matter transporter, Squidward's arm is on the left, and SpongeBob's arm is on the right. Later on at the Krusty Krab, in the shot after Mr. Krabs tells both of them, "Alright, that's it!", we can see that both arms are SpongeBob's, when the left one is supposed to be Squidward's. (00:17:42)
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: Bubblestand: When SpongeBob comes out of his house at the beginning, he leaves his front door open. Later on, when Patrick's rock opens up, the front door to SpongeBob's house is completely missing. Then, when SpongeBob hands Patrick the bubble wand, the door is back, and it is now closed. Finally, when SpongeBob and Patrick walk into the house later on, the door is open again. (00:02:30)
Hall Monitor / Jellyfish Jam - S1-E7
Continuity mistake: Hall Monitor: When SpongeBob sees the open window to the house, the window is opened to the left. When the two fish run out of the house after SpongeBob scares them, the window is opened the opposite way, then reverts back in the next shot. (00:05:19)
New Student Starfish / Clams - S3-E14
Continuity mistake: New Student Starfish: Spongebob shows Patrick the Good Noodles board when they enter the classroom. Then when Patrick is trying to tell the class his name, the number of stars on it change, and the name "Rich" appears on it, which wasn't there before. Later on, when Spongebob and Patrick are in detention, the names on the board are completely different in some shots. (00:02:48 - 00:11:24)
Continuity mistake: Rock Bottom: When the cardboard version of Spongebob next to the candy machine is shown, it is frowning, but it turns into a smile when it falls over. (00:18:48)
The Thing/Hocus Pocus - S4-E16
Continuity mistake: The Thing: When Squidward is riding his bike on the road, he hits a cement truck, and gets covered in cement. He tries to get out of it, and a shot later, the location suddenly changes from the road to a green hill. (00:04:05)
Whatever Happened to SpongeBob? (WhoBob WhatPants) - S5-E18
Continuity mistake: Near the beginning, Spongebob picks up Gary, and some of his slime falls on the floor. When he hugs him and breaks his shell, the slime is gone. (00:01:56)
Picture Day/Pat No Pay/Blackjack - S5-E13
Continuity mistake: When Patrick picks up the fridge and throws it on the barrel, there is some metal on the floor. When Mr. Krabs walks into the kitchen 2 seconds later, there is no metal on the floor.
Continuity mistake: When Patar heats the squished crab in the fire, it's in his left hand. But in the next shot when he eats it, it's in his right.
Wet Painters / Krusty Krab Training Video - S3-E9
Continuity mistake: When Mr. Krabs Gets Home, there is a light switch by the door, but in the next shot there is a sign instead.
Krab Borg / Rock-a-Bye Bivalve - S3-E8
Continuity mistake: Rock-a-Bye Bivalve: When Patrick gets home from the party after midnight SpongeBob is angry, and as Patrick walks out in the interior shot the front door is wide open on the inside of the home, but in the next exterior shot the front door is wide open on the outside of the pineapple.
Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: Mermaid Man and Barnacle Boy IV: When SpongeBob runs into the kitchen with Mermaid Man's secret utility belt, the door swings open facing away from the grill, but when Squidward demands to know what's going on in the kitchen, the door opens the opposite way.
Answer: I believe this is the Season 6 episode "Spongicus".