New Digs / Krabs à la Mode - S5-E6
Continuity mistake: In "Krabs à la Mode", Spongebob is wearing miniature mittens on his eyelashes while walking to the Krusty Krab. They disappear after a few shots.
Roller Cowards / Bucket Sweet Bucket - S5-E8
Deliberate mistake: In 'Bucket Sweet Bucket' there's no way that Plankton managed to reach with his paint brush to repaint the entire front of his establishment from the top of Squidward's head.
The Original Fry Cook / Night Light - S5-E9
Continuity mistake: Near the end of "Night Light" Patrick gets burned by the sun, and the wooden stem atop his house is missing.
Money Talks / SpongeBob vs. The Patty Gadget / Slimy Dancing - S5-E10
Audio problem: In "Slimy Dancing" in the scene where Squidward and Spongebob perform their act, we first see Squidward making Spongebob spin around. There's a shot where it shows Squidward inside Spongebob. The curtain in the background in the shot remains still, even though you can hear spinning.
A Flea in Her Dome / The Donut of Shame / The Krusty Plate - S5-E11
Continuity mistake: In "A Flea in Her Dome", Patrick asks Spongebob to get on Sandy's shoulders. Then, he climbs onto Spongebob's shoulders. In the next shot, they are suddenly next to Sandy's tree.
A Flea in Her Dome / The Donut of Shame / The Krusty Plate - S5-E11
Continuity mistake: In "A Flea in Her Dome", Patrick gets bitten by a flea and his chest is covered in bites. He takes out a pencil and connects some of the dots to make a horse. A few shots later, the horse and the bites disappear.
A Flea in Her Dome / The Donut of Shame / The Krusty Plate - S5-E11
Factual error: In 'A Flea in Her Dome' Sandy opened up the door for water to fill her dome. The water even replaced the air on the inside which was above the door, which isn't possible because the air would have to go down through the door to escape the dome.
A Flea in Her Dome / The Donut of Shame / The Krusty Plate - S5-E11
Continuity mistake: In "The Krusty Plate", Spongebob finds that one plate has a brown smudge on it. After an attempt to clean the plate, he lifts it up and the smudge is now a light shade of green.
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)
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.
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.
Atlantis SquarePantis - S5-E12
Continuity mistake: When Plankton is placed in a jar, there is a sign that says "No Flash Photography" above him. In the next shot, this sign disappears.
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.
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.
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.
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.
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.
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.
Answer: I believe this is the Season 6 episode "Spongicus".