Karen 2.0/InSPONGEiac - S8-E28
Continuity mistake: Squidward's house is missing in the shot that shows SpongeBob running from his house to Patrick's house.
Spongebob's Last Stand - S7-E22
Continuity mistake: As soon as a man stamps on a tambourine, it disappears 2 shots later.
Born to Be Wild/Best Frenemies - S4-E18
Continuity mistake: When we first see Plankton, the distance between him and the Kelpshake store keeps changing between shots. (00:02:20)
Pressure / The Smoking Peanut - S2-E12
Continuity mistake: In the episode "The Smoking Peanut" At the end when the man holds up the pearl out of Mr. Krabs pocket, despite being surrounded by a stadium, the close-up of his hand shows complete blue sky in the background.
Chocolate With Nuts / Mermaid Man And Barnacle Boy V - S3-E11
Continuity mistake: When Barnacle Boy and E.V.I.L. are hiding behind the rock you can see Barnacle Boy's fingers. In the next shot he is wearing gloves.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: In the episode "Pickles", there is a large fish named Bubble Bass. Although his name is Bubble Bass, the captions say his name is Bubble Bath. It is clear that Spongebob is saying "Bass" not "Bath", and his name is given as Bubble Bass in SpongeBob's Diner Dash.
Krab Borg / Rock-a-Bye Bivalve - S3-E8
Continuity mistake: In "Rock-a-Bye Bivalve" when Spongebob and Patrick hear the bivalve chirping, the coral that vibrates is bright green and is standing up straight. However, when they find the bivalve and take it out from behind the coral, the coral is dark green and is bent over.
The Great Snail Race / Mid-Life Crustacean - S3-E15
Continuity mistake: When Squidward looks through a window of SpongeBob's house, Patrick looks through a higher window. An outside shot shows that Patrick is standing in Squidward's shoulders, however, an inside shot shows that Patrick isn't in Squidward's shoulders.
Pre-Hibernation Week / Life of Crime - S2-E13
Continuity mistake: When Spongebob falls off the sea needle, he lands on a . It shows his ripped off skin, then it shows his back with the piece missing, but the shapes are different.
Sandy, SpongeBob and the Worm / Squid on Strike - S2-E18
Continuity mistake: When Spongebob shows Sandy the paper clip and a piece of string the string is very small. Yet later after Sandy says, "no silly, how about s for saving our skins", the string is a lot longer.
SpongeBob Meets the Strangler / Pranks a Lot - S3-E20
Plot hole: In the end of "Pranks A Lot" SpongeBob and Patrick glue the door shut in order to keep Mr. Krabs inside the Krusty Krab. When SpongeBob And Patrick are visible again, it turns out that a lot of customers have entered the Krusty Krab to see SpongeBob and Patrick naked. All of those people had no way to get into the Krusty Krab with the doors glued shut. It can't be that they broke down the doors, as they're still there.
Suggested correction: Mr. Krabs most likely washed the glue off the doors and let the people in.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Character mistake: In 'Welcome to the Chum Bucket', Spongebob said he likes the grill facing the wall to the right. Plankton pushes it so that it is facing the wrong wall, the wall on the left.
MuscleBob BuffPants / Squidward, the Unfriendly Ghost - S1-E11
Continuity mistake: When Patrick throws Squidward the watermelon, it lands on his torso and he falls down. When the camera goes back to Squidward, the watermelon is in his mouth.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Help Wanted" Gary doesn't have eyelashes. In every other episode he does.
Suggested correction: So Gary not having eyelashes could count as an early design for him. It's common that characters and environments may undergo changes after a pilot. Not a mistake.
But Gary never had eyelashes.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: At the end of "Welcome To The Chum Bucket", look at Spongebob's eyes. His eyebrows are more far apart than usual, also his eyeballs are uneven a bit.
Patrick SmartPants/SquidBob TentaclePants - S4-E8
Continuity mistake: When SpongeBob and Squidward are combined, Squidward's arm is on the left and SpongeBob's arm is on the right, and that's how it is the whole time. Except in one shot, the shot of SpongeBob's head after Squidward says, "yellow freak." Look at the bottom and you'll see two SpongeBob arms, when the one on the left is supposed to be Squidward's.
Born Again Krabs (aka A Penny Saved) / Safety Freak (aka I Had An Accident) - S3-E17
Audio problem: At the end of "Born Again Krabs", SpongeBob is talking to The Flying Dutchman on the phone. SpongeBob's dialogue isn't in sync with his mouth.

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."
Procrastination / I'm With Stupid - S2-E19
Other mistake: I'm With Stupid: When Patrick and his "parents" make fun of Spongebob because they believe he's stupid, he gets so frustrated that he runs through the wall, leading him right outside. This makes no sense, because they are in Patrick's house and the inside of it is underground. (00:21:35)
SpongeBob Meets the Strangler / Pranks a Lot - S3-E20
Other mistake: Pranks a Lot: When everyone is cheering on Spongebob and Patrick at the end, Sandy whistles by putting her hand through her helmet. Impossible. (00:23:30)