Atlantis SquarePantis - S5-E12
Revealing mistake: Atlantis SquarePantis: After the Atlantis van crashes through the museum's ceiling, Squidward is surprised that it's the magical path to Atlantis, and while Krabs says, "Nice hot rod flames," note how only the disembodied tip of Patrick's arm clips in front of SpongeBob's body (it even moves as Patrick moves), due to an animation error in this shot. (00:09:55)
Continuity mistake: When Mr. Krabs' ancestor eats SpongeBuck's chilli he takes a spoonful and spits it out. In the next shot of SpongeBuck, chilli is all over is face, but he didn't spit out that much chilli to have his entire face covered.
Rise and Shine / Waiting / Sing a Song of Patrick - S5-E1
Continuity mistake: In "Sing a Song of Patrick", Patrick creates his own song and listens to it with Spongebob in his pineapple. And at the end of the song the pineapple melts and the stereo falls on top of them and not the pineapple. But when they get up, the busted stereo disappears and the pineapple is on top of them.
Spy Buddies / Boat Smarts / Good Ol' Whatshisname - S5-E4
Continuity mistake: At the beginning of Spy Buddies, when Mr. Krabs is entering the code to enter the Krusty Krab, it's night. But when Patrick yells about him wanting to be a spy and it shows the fish walking outside of the Krusty Krab, it is day.
20,000 Patties Under the Sea/The Battle of Bikini Bottom - S5-E17
Audio problem: In "20,000 Patties Under the Sea" When Plankton says "Ah who needs that rustbucket anyhow!" his mouth is way out of sync.
Atlantis SquarePantis - S5-E12
Continuity mistake: When SpongeBob and Patrick are in the cave, the points on the amulet change size and shape between shots.
20,000 Patties Under the Sea/The Battle of Bikini Bottom - S5-E17
Continuity mistake: In one scene where Spongebob is breathing in air, you can see the container to the right is yellow, but in the scene where he's dancing around the kitchen, it turns white.
Other mistake: In the one scene, Mr. Krabs and Plankton notice Stinky Burgers was shut down. When it cuts to their reactions, Mr. Krabs' eyebrows are missing.
Continuity mistake: When Krabs', Squidward's and Puff's ancestors attempt to flee with the coach they pass way more buildings, seen in the background, than there actually are as shown in the overhead view of the town.
Blackened Sponge/Mermaidman vs. SpongeBob - S5-E14
Continuity mistake: In 'Blackened Sponge' a flap door suddenly appears on Spongebob's bedroom door in the background as Gary goes away to laugh.
Picture Day/Pat No Pay/Blackjack - S5-E13
Continuity mistake: In 'Picture Day' the second time Spongebob paints on the stripes on his socks they disappear in the shot where he paint rolls on his shirt/pants.
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: Banned in Bikini Bottom: After the police raid the Secret Krusty Krab, Krabs and SpongeBob are both in handcuffs, but when Miss Gristlepuss trips and the Krabby Patty falls into her mouth, both pairs of handcuffs have vanished, then the handcuffs reappear again on Krabs. (00:09:45)
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: Stanley S. SquarePants: When Stanley's first customer tries to place an order Stanley pulls out a camera on a tripod, and in the next shot as Stanley hugs the customer for their first picture, the kitchen door behind them does not have the usual porthole, instead it has an anchor on it just like the door to Krabs' office. (00:19:15)
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: Stanley S. SquarePants: When SpongeBob introduces Squidward to his cousin, Squidward's moai house has a doorknob at the right side of the door, but when Squidward loads the back of the moving truck the doorknob is at the left side of the door. (00:14:15)
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: Banned in Bikini Bottom: After the chief of police tells his wife that he's starving he speeds off, and when it cuts to a closeup of the lock and chains, the wood plank directly behind the chains is crossed from upper right to lower left, but in the next shot it's crossed the opposite way. (00:05:40)
The Inmates of Summer/To Save a Squirrel - S5-E15
Continuity mistake: In "The Inmates of Summer", the campers that board the boat while Spongebob and Patrick are crying together throw confetti that lands on top of their puddle of tears. When the inmates start boarding in a few shots, a wide shot shows the confetti has disappeared and the next shot, which is closer, also shows the confetti to have vanished.
The Inmates of Summer/To Save a Squirrel - S5-E15
Continuity mistake: In "To Save a Squirrel", Sandy has oil stains all over her suit from working on her vehicle. After she is tackled by Spongebob and Patrick when they were chased by a grasshopper in two shots, the stains disappear.
The Inmates of Summer/To Save a Squirrel - S5-E15
Continuity mistake: In "To Save a Squirrel", Spongebob is slowly losing his mind in the mud replica of the Krusty Krab and he begins to make a fake Krabby Patty out of mud. He says he needs buns and suddenly two pieces of rock appear next to him that weren't there before.
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: In Stanley S. Squarepants, when Squidward moves out of the house with all his bags he doesn't shut the door, but when the shot zooms out, it's shut.
Atlantis SquarePantis - S5-E12
Continuity mistake: When Patchy finds Encino to have shrank, he hits his peg leg against his foot. When Encino is being turned back into normal, he is wearing shoes on both feet.
Answer: I believe this is the Season 6 episode "Spongicus".