Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: Boating School: When SpongeBob remembers that it's the day of the boating exam, the calendar reads "boating exam today," but then it reads "driving exam today."
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)
Patrick SmartPants/SquidBob TentaclePants - S4-E8
Plot hole: In 'Patrick SmartPants' Patrick lost the top of his head after falling off a cliff, but Spongebob put it back on. Suddenly Patrick's intelligence skyrocketed, but wanted to return to his former self in the end of the episode. To do this he re-enacted his fall, but it was unsuccessful. They eventually figured out that Spongebob had in fact not put on Patrick's head, but a 'brain collar'. How did Patrick posses his memories throughout the 'intelligent phase' despite not having his own head (and brain)?
The Snowball Effect / One Krabs Trash - S3-E3
Other mistake: In 'The Snowball Effect' when Squidward attempts to make Patrick and Spongebob resume their snowball fight he throws a snowball at them which they avoid, and it puts out Squidward's fire inside. Squidward had his back towards his house and threw the snowball in the opposite direction.
You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Deliberate mistake: Spongebob gets stuck in the top of a tree as Gary removes the ladder. In previous episodes it's quite clear that he's more than willing to 'fall' as he takes no damage when hitting the ground due to the low fall speed.
Other mistake: At the very end, Sandy puts Wormy inside of a glass jar. Not only does she break the bubble surrounding it, there's no way for water not to enter the jar as she holds it sideways. Wormy should be killed.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: The pencil's length in 'Frankendoodle' varies in between above and beneath the water surface.
Deliberate mistake: Spongebob blew a bubble to capture the butterfly while wearing that fishbowl on his head.
House Fancy/Krabby Road - S6-E1
Continuity mistake: Plankton's size changes drastically throughout Krabby Road. Plankton can be seen as reaching up to Spongebob's waist at one point. When he's clutching to the neck of a guitar, the amount of frets that go into his height change between one, two, three, and five, depending on the shot. (00:02:10)
Continuity mistake: When Mr. Krabs and SpongeBob are standing in front of the bomb after it lands but doesn't go off, the clock inside Mr. Krabs' office can be seen from the kitchen. The time on the clock is 5:00, but in the next shot, the time on the clock is suddenly 3:00. The bomb is then revealed to be a mechanical hand, and the time on the clock is now 5:00 again.
Continuity mistake: When SpongeBob accidentally reveals the location of the formula, Plankton drops the feather he is holding and lands in front of him. The feather remains on the floor, but when Pearl walks into the kitchen, the feather has suddenly vanished, and reappears in front of Plankton in the next shot.
Continuity mistake: When Plankton is telling Karen, "There's a whale in the laboratory," he is jumping up and down with his arms in the air, but in the next shot, his arms are suddenly down at his side.
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.
New Fish in Town/Big Sister Sam - S8-E10
Audio problem: In "New Fish in Town", Squidward pops out of his door and says "the bassoon." When he says it, the words are heard, but his mouth movements are delayed.
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.
Continuity mistake: In "Once Bitten", Mr. Krabs is holding a key, about to unlock the doors to the Krusty Krab, when a customer stops him. Two shots later, the key is missing from his hands.
Krusty Towers/Mrs. Puff, You're Fired - S4-E9
Continuity mistake: When the rocks fall out of Patrick's suitcase, the rocks change number and position between the 3 shots.
Answer: I believe this is the Season 6 episode "Spongicus".