Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Plankton! When Plankton pulls out a radio player to play his evil music on SpongeBobs pillow, it has disappeared when Spongebob wakes up. SpongeBob didn't move on it.
Continuity mistake: When all of Spongebob's friends are formed around him, there's one scene where Pearl's hat disappears and then reappears, so for a few seconds she's completely bald. Her hair isn't even there.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Jellyfishing, when Patrick puts the net in Squidward's hand, at first it is in his left hand, but when he gets the jellyfish on the king jellyfish, it is on his right hand.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: Spongebob crashes through Squidward's house, and his bedroom is on the bottom floor. But in "Shanghied" after Squidward exits the fly of doom, you can see his bedroom is on the top floor, as it is in other episodes.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: In "Bubblestand" after Squidward blows the huge bubble, he tells Spongebob and Patrick that the ability to blow bubbles is in his genes. If you look at the position of the bubblestand sign, the sign is facing the direction Squidward is talking. The sign had always been facing the street, which means that Squidward was actually talking towards the street, when Spongebob and Patrick are actually to his right.
Hall Monitor / Jellyfish Jam - S1-E7
Continuity mistake: When SpongeBob asks Squidward to play his clarinet better, he is wearing his night shirt which is purple, but in the next shot he is wearing his normal shirt which is brown.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Plankton, when SpongeBob steps on Plankton, he steps on him with his left foot, except he pulls Plankton off of his right foot.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: When Spongebob first shows Patrick the technique for bubble-blowing, there are two red corals in the background - one on his right and one on his left. Later, when he shows Squidward the technique, the red coral on the left side of the screen disappears.
The Chaperone / Employee of the Month - S1-E12
Continuity mistake: When Spongebob is talking about Annoy Squidward Day, you see a calendar with 28 days, indicating that it's February, but the empty picture on the wall says January.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Jellyfishing, when SpongeBob and Patrick first take their nets to jellyfishing, they only take their own nets. But when they go to Squidward's house, they have another net, just for him.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: In the scene where Squidward complains to Spongebob about the construction noise from his stand, Squidward's porthole in the background is black, but from the interior there is a light on (Note: this also happens in every other shot of his house.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: SpongeBob takes off his ripped pants, and throws them on the ground. His shirt sleeves are perfectly intact. Next, Sandy and Larry are shown playing volleyball. When SpongeBob is shown again, his pants are still gone, and so are his shirt sleeves.
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.
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.
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.
Answer: I believe this is the Season 6 episode "Spongicus".