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.
MuscleBob BuffPants / Squidward, the Unfriendly Ghost - S1-E11
Other mistake: When Squidward is on the royal bed, Spongebob's Pineapple is nowhere in sight.
Banned in Bikini Bottom/Stanley S. SquarePants - S5-E20
Continuity mistake: In Stanley S. Squarepants, when SpongeBob and Stanley go see Squidward when he's getting the newspaper, both Squidward and the newspaper change position in between shots.
Club SpongeBob / My Pretty Seahorse - S3-E12
Continuity mistake: In "My Pretty Seahorse", Spongebob is using a spatula with slots in it. Later, when Mystery eats it, the spatula is now completely flat.
Culture Shock / F.U.N. - S1-E10
Continuity mistake: In "F.U.N.", Mr. Krabs sets down the Krabby Patty in front of Plankton. Almost the whole plate is on the yellow part of the table, but when the camera cuts to Plankton, the plate is mostly in the red part of the table. In the next shot, the plate returns to its original position.
Squidtastic Voyage/That's No Lady - S4-E15
Continuity mistake: In "That's No Lady", Patrick runs through Spongebob's wall, leaving a Patrick-shape in his house. Patrick pushes a bit of Spongebob's house, which disappears in the next shot.
Ghoul Fools - S8-E24
Continuity mistake: When Squidward is sucked into "The Void", the bag of money that he was holding vanishes in the next shot.
Audio problem: When Spongebob, is in the pile of rubble left after Squidward unraveled, he picks up his phone receiver. Then, Gary slithers away and you hear Spongebob pressing the keys on the phone, but when it cuts back to him, he is only holding the receiver.
Summer Job - S7-E18
Continuity mistake: Mrs. Puff didn't know that SpongeBob works at the Krusty Krab, when she already found out in 3-18 "Krusty Love." Even stranger thing, Mr. Krabs and Mrs. Puff have no idea who each other are, but they also already met in that episode.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: In "Fools in April", Spongebob is scrubbing the floor and a customer comes up to him to ask for a couple of ice cubes. In the next shot, the water puddle on the floor gets increasingly bigger.
Continuity mistake: In "Jellyfishing" when Squidward gets home from the hospital, Patrick exclaims Merry Christmas! However, later on in the series it is revealed that nobody in Bikini Bottom even knew what Christmas was.
Suggested correction: The episodes are not always meant to be in chronological order. It's entirely possible that "Christmas Who?" took place before "Jellyfishing."
The Bully / Just One Bite - S2-E17
Continuity mistake: In the episode "The Bully," when Flats punches Spongebob, Spongebob states to Gary that he's made out of some spongy material, that it absorbs his blows and it doesn't hurt him at all. But in later episodes, when Spongebob gets knocked out that never happens anymore.
Procrastination / I'm With Stupid - S2-E19
Continuity mistake: Procrastination: When Gary eats all the food, he burps out his bowl. A ladder suddenly appears next to it.
Plot hole: After being spared, Medieval Sandy announced that she will help in the defeat of medieval Plankton. How did she know what they were planning?
Big Pink Loser / Bubble Buddy - S2-E3
Revealing mistake: Big Pink Loser: When Patrick is answering phone calls, the third time he picks up and says, "No, this is Patrick", the anchor symbol on his hat briefly vanishes. (00:04:36)
Suggested correction: This mistake can only be detected by freezing the film and advancing frame by frame. It is not visible while watching the film at a normal running speed. According to the rules of this site, this invalidates the error.
So, I reworded the mistake to say that it "briefly vanishes," because it's actually gone for a few frames, not one. I did not advance frame by frame to find the error. If you watch the scene at normal speed, it disappears for a brief moment, then comes back. I assume this correction might have been made without watching the scene, especially since the show was referred to as a "film."
This is not true. You can see it disappear if you watch it at normal speed; it does not require pausing at all. At least, I am able to see it.