Texas / Walking Small - S1-E18
Continuity mistake: In "Walking Small", The eel that stole Spongebob's ice cream cone throws it at his face. Different shots some show ice cream on Spongebob's nose, and some show that Spongebob's face is clean.
Sandy's Rocket / Squeaky Boots - S1-E8
Audio problem: In "Sandy's Rocket", when Sandy says "Aliens? Is that what this is about?" her mouth stops moving halfway into her sentence.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Help Wanted", the last time SpongeBob says "I'm ready!", his collar turns red.
MuscleBob BuffPants / Squidward, the Unfriendly Ghost - S1-E11
Plot hole: In MuscleBob BuffPants, when SpongeBob first shows off his new inflatable muscles to everyone on the beach, he had the strength to punch two muscular fish into the air with them. A minute later, he could not even lift a glass of juice with the inflatable muscles. (00:04:25 - 00:05:20)
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Character mistake: In "Help Wanted", Stephen Hillenburg's name in the "Written By" section of the title card is incorrectly spelled as "Stephen Hilleburg."
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.
Revealing mistake: After SpongeBob disguises himself as Patrick's rock and right before he sneezes his uvula clips through his bottom lip.
Sandy's Rocket / Squeaky Boots - S1-E8
Audio problem: When SpongeBob captures Mrs. Puff, her voice and the inflation sound are out of sync.
Continuity mistake: Rock Bottom: After SpongeBob and Patrick enter the bus, when SpongeBob asks Patrick if he has any change and for the duration of this shot, both the gear shift on the floor beside the driver and the open door of the bus have vanished, then they reappear.
Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: Hooky: When SpongeBob is hooked the pointy tip of the hook is facing out, but when he asks Krabs what he should do, the hook is hooked into SpongeBob's pants the opposite way, with the pointy tip facing him. Additionally, he's hooked at the back of his underwear and pants, but when Squidward is holding the fishing pole the hook is at the front of the underwear, which are also perfectly intact despite being ripped off SpongeBob.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: Fools in April: While Squidward is having difficulty apologizing to SpongeBob, they're both standing in front of the pineapple with its front door wide open inward, but when Squidward places the bubble over his head the front door is suddenly wide open outward, so Squidward could slam the door.
Valentine's Day / The Paper - S1-E16
Continuity mistake: The Paper: The front door of Squidward's house repeatedly switches between opening at the right side and opening at the left side, and the round door knob also changes to a door handle as well, but then reverts back to the round knob.
SB-129 / Karate Choppers - S1-E14
Continuity mistake: SB-129: When Squidward opens the door to the time machine, the exterior side of the door has a handle at the left side and opens at the left, but the interior side of that door also has the handle at the left side, though it should be at the right side. Then when Squidward activates the machine, the exterior handle is now at the right side and it opens at the right.
Nature Pants / Opposite Day - S1-E9
Continuity mistake: Opposite Day: The front door knob on Squidward's house repeatedly switches between the left and right side of the door, so it opens the opposite way (it has nothing to do with it being opposite day).
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: Mermaid Man wears green tights, but after SpongeBob absorbs the water ball like "some kind of evil sponge," when Mermaid Man and Barnacle Boy start doing the dog paddle, Mermaid Man's tights have vanished in this shot.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When Barnacle Boy opens the box with the two rings inside, in the closeup the "B" ring is on the left and the "M" ring on the right, but in the wideshot Barnacle Boy removes the ring on the left (the "B") and places it on Mermaid Man's finger, then in the next shot we see it's the "M" ring, before both rings vanish.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When SpongeBob and Patrick (dressed in their superhero costumes) exit the pineapple the front door opens at the right side (outward), but after getting on Squidward's nerves, when they retreat back inside the front door opens the opposite way at the left side (inward).
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Revealing mistake: In the shot where Spongebob says, "That little squirrel is in trouble, " half of his belt is missing.
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: Spongebob's belt is missing when his clothes are first revealed while dangling in midair.
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: The Krusty Krab is filled with Halloween decorations during the episode, but when Spongebob jumps to hide in a barrel there are no decorations in sight.
Answer: I believe this is the Season 6 episode "Spongicus".