Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: In "Hooky," when Spongebob gets hooked, the hook changes from dark yellow, to dark pink, to dark blue in between shots.
Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: The track changes between days.
Valentine's Day / The Paper - S1-E16
Continuity mistake: In "Valentine's Day", Patrick starts searching his present in the fair. Then he goes to a mountain and falls thinking that there will be his present. This mountain wasn't there before, even when they arrived to the fair.
Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: When Patrick runs out of Spongebob's house after Spongebob cries and says he's cheating, the lower right window beside the door is gone.
Naughty Nautical Neighbors / Boating School - S1-E4
Continuity mistake: When Squidward starts making pink bubbles with messages, he goes to his backyard. Notice he never closed the back window of his house. When he starts laughing because of the messages, suddenly the window is closed. After Patrick saves Squidward, the window is still closed, but when they go to the front of his house, the window is open.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In "Plankton", when Plankton is controlling Spongebob, Spongebob goes to put his pants on, but Plankton has him walk through them. As they're walking towards the pants, the tie is red. As they're walking through the pants, the tie turns black. As they walk away from the pants, the tie is red again.
Sandy's Rocket / Squeaky Boots - S1-E8
Continuity mistake: Sandy's Rocket: When you first see SpongeBob in bed you can see a mysterious glass window on the floor. When Patrick arrives it has vanished, evident in the wide shot.
MuscleBob BuffPants / Squidward, the Unfriendly Ghost - S1-E11
Continuity mistake: When Squidward comes out of the bathroom and sees his melted sculpture, the eyes on the melted sculpture change from looking on the floor to looking up in a matter of seconds.
Continuity mistake: In "Suds" after Spongebob crashes through his bedroom window, the blanket is hanging over the side and is all wavy, but when he's in bed it's completely plain and doesn't hang over the sides.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Reef Blowers," when Spongebob is flying back from the rope he is pulling, Squidward is nowhere to be seen. When the ocean is getting drained, Squidward is sitting on his porch.
Valentine's Day / The Paper - S1-E16
Continuity mistake: In Valentine's Day, almost at the end, Patrick smashes some presents with his foot. After a while, Sandy arrives with Patrick's present (a chocolate globe), and you can see that the presents have disappeared.
Valentine's Day / The Paper - S1-E16
Continuity mistake: In "Valentine's Day", SpongeBob and Patrick arrive at the fair. They watch the fair. Patrick says "You bought me a fair?", and Patrick runs to the fair. When he starts saying, "Get out of my fair.", we see that SpongeBob is closer to the fair than he was before.
Nature Pants / Opposite Day - S1-E9
Continuity mistake: When Spongebob goes to answer his door, Patrick was obviously in front of the door. After Patrick says, "Spongebob doesn't like me anymore", it cuts to a different shot to show the outside of the front door, and Patrick has moved to the side of the door.
Continuity mistake: In "Sleepy Time" when the neighbours are crowded around Spongebob, Plankton is standing on the end of the bed. When the angle changes, he's gone. Then he jumps onto the bed before Patrick joins them.
The Chaperone / Employee of the Month - S1-E12
Continuity mistake: Spongebob absorbs the pink punch making him look pink in 2 shots - one showing him squirting punch out of his nose, but a shot after that shows him yellow.
Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: In the beginning of Hooky, there are about three boats with 3 fisherman in each. That means there would be 9, but later there are dozens.
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.
Continuity mistake: Rock Bottom: When the cardboard version of SpongeBob next to the candy machine is shown, it is frowning, but it turns into a smile mid-shot when it falls over. (00:18:48)
Hall Monitor / Jellyfish Jam - S1-E7
Continuity mistake: Hall Monitor: After SpongeBob walks out of class the bell rings and he gets trampled, and when Mrs. Puff follows him outside the classroom door is wide open, but then the entire door suddenly vanishes.
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."
Answer: I believe this is the Season 6 episode "Spongicus".