Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: When Spongebob takes his outer suit/pants off and finds out that the hook is stuck through his underpants, Mr. Krabs places a Help Wanted sign up on the front door of the Krusty Krab. When Spongebob crashes onto the doors naked, the sign disappears.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In 'Plankton', when Spongebob is being controlled by Plankton and he bounces into the wall in the Chum Bucket, he is tumbling in a way so that when he is standing, he is facing away from the ingredient identifier. When the shot changes, Spongebob is now facing the identifier while standing.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: The words "Total Control" constantly appear and disappear from the controlling device in Spongebob's brain.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: When Spongebob grabs Squidward's legs you only see him grabbing at two of Squidward's legs and the other two legs have disappeared, but when the shot changes they're back again.
The Chaperone / Employee of the Month - S1-E12
Audio problem: We see Spongebob in his long legs walk over to Mr. Krabs' house, then we see the door from inside the house. Through the window we see Spongebob's long legs, yet we hear him spring boing his way over when we see them already there.
Hall Monitor / Jellyfish Jam - S1-E7
Continuity mistake: In "Jellyfish jam", when SpongeBob shows the jellyfish to Squidward, and the jellyfish starts to do a lot of things, you see that Squidward is looking by his porthole in his house. The porthole is closed. However, when he says "How can anybody have fun with a jellyfish?" his arms go outside the porthole. But this is impossible, since the porthole is closed.
Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: In 'Boating School' when Mrs. Puff blows up she has a deep voice, but in all the other episodes her voice stays the same.
Revealing mistake: Near the end of "Rock Bottom", when SpongeBob arrives back to Bikini Bottom, SpongeBob's pineapple is animated differently from the other buildings. It looks like it was cheaply tacked on in post production.
Continuity mistake: Sleepy Time: When everyone woke up SpongeBob near the end, Pearl is seen without her ponytail, but in the next shot, she has a nightcap on.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: In "Neptune's Spatula", Patrick takes a picture of SpongeBob holding the spatula. When this happens, we can see that SpongeBob is a little worried because clouds have appeared there. However, after a while, Patrick shows the picture to Neptune, and we can see that in the picture SpongeBob is smiling and pointing with the spatula.
SB-129 / Karate Choppers - S1-E14
Continuity mistake: When Spongebob throws the Krabby Patties on Squidward's head there are only 6 of them, later there's at least 8.
Pizza Delivery / Home Sweet Pineapple - S1-E5
Audio problem: In "Pizza Delivery," when you see them being sucked towards the whirlpool (wide shot of whirlpool). Squidward says, "Let go of the pizza." several times before they actually get caught up in the whirlpool. But the time where he says the line and it automatically cuts to his face, when you see his face, it is the end of him saying the line so you hear, ".izza." You hear that, but when you see a close up of his face, his mouth is completely shut.
Continuity mistake: In "Rock Bottom" when Spongebob is on line and the egg cracks, you can see the cracked pieces on the ground and then when he does his (in pants) "Barnacles, tartar sauce" you can't see the egg pieces.
Sandy's Rocket / Squeaky Boots - S1-E8
Continuity mistake: In "Squeaky Boots", Mr. Krabs starts hearing squeaky sounds everywhere. Then he goes mad and says he took the boots from SpongeBob. At this point, notice the restaurant floor's colour. Mr. Krabs lifts the whole restaurant, but we can still see some floor (where Krabs is). Notice that now the colour of the floor has changed.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Audio problem: When Bubble Bass runs out of the Krusty Krab he is gasping and panting, but his mouth stays closed, his mouth doesn't even open a centimeter.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: At the beginning of "Mermaid Man and Barnacle Boy", when SpongeBob and Patrick are watching TV viewing Mermaid Man and Barnacle Boy show, you can see that these heroes have 5 fingers on their hands, as the real human beings. However, when SpongeBob and Patrick meet these heroes, as in the rest of the show, you can see that now, the heroes, have 4 fingers on their hands, as cartoon characters usually have.
Sandy's Rocket / Squeaky Boots - S1-E8
Factual error: Sandy's dome is both airtight and watertight to keep any water out of the dome and any air inside the dome. When the rocket, positioned outside of the dome, begins to launch, smoke is coming inside the dome. This shouldn't be able to happen if the dome is airtight and watertight.
Hall Monitor / Jellyfish Jam - S1-E7
Continuity mistake: In episode 1-7, Hall Monitor, Patrick says Spongebob is at the intersection of Conch and Coral, and we then see the street sign. However when we see Spongebob standing on the road, there is only one road, and no intersection.
SB-129 / Karate Choppers - S1-E14
Continuity mistake: When Squidward is in the white place and crashes through the floor, he doesn't have his clarinet before he crashes through the floor. But when he is in the time machine, he has his clarinet.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In "Plankton", when Plankton says tomorrow is his birthday, he is near Spongebob's thumb. When the camera zooms in on Plankton, he is instantly in the middle of Spongebob's hand.
Answer: I believe this is the Season 6 episode "Spongicus".