The Graveyard Shift / Krusty Love - S3-E13
Continuity mistake: When SpongeBob is cleaning the roof, you can see that there isn't nothing up there. The very next shot shows a closer view to SpongeBob and we can see that is a bucket there. That wasn't there before.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: Frankendoodle erases the door in SpongeBob's house (when they're fighting in the night). A few moments later you see the door is back.
Chocolate With Nuts / Mermaid Man And Barnacle Boy V - S3-E11
Continuity mistake: When SpongeBob and Patrick are pretending that they need an operation and that fish falls down the stairs, if you look at Patrick's head he has no bandage on his head. But when he looks at SpongeBob right after that fish falls down the stairs, a bandage suddenly appears on his head.
Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: When mermaid man and barnacle boy are looking for the invisible boatmobile, there are boats all over, even in front of the windows, but when Spongebob is inside running towards the door there are now no boats visible out the window.
Continuity mistake: When Patchy lifts his eye patch to rub his eye and puts the patch on his right eye. In the next shot the patch is on his left eye.
Krab Borg / Rock-a-Bye Bivalve - S3-E8
Continuity mistake: In the scene where SpongeBob has given his pants to the clam, two continuity errors appear. First, Patrick puts his head in the pants and he says that the clam is hungry. A lot of holes are in his head. In the very next shot, the holes are gone. This is really obvious. The other continuity error is that before Patrick gets those holes, SpongeBob isn't with his pants. When he tries to give the Patty to the clam, he's suddenly with his pants, when the little clam is supposed to have his pants.
The Sponge Who Could Fly (aka The Lost Episode) - S3-E16
Continuity mistake: When the tape pours out of the VCR at the end of the show, Patchy the Pirate gets tangled in it. A shot later, the tape is three times longer than it was the shot before it.
No Weenies Allowed / Squilliam Returns - S3-E6
Continuity mistake: In "Squilliam Returns", when Squilliam arrives at the "5-star restaurant" it is nighttime, but at the end when Squidward says "Will you get out of here!" to Mr.Krabs and it zooms out on the Krusty Krab it is daytime.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In "The Snowball Effect", sometimes Squidward's doorknob is on the left, and sometimes it's on the right.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In "The Snowball Effect" when Patrick tries to make a snowball the third thing he makes is a DNA strand, if you look closely, when it is in closer, the DNA strand is shorter than when they go out on it.
Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: At the start of MMIV, SpongeBob rips off a person's pocket to get a pen. He totally rips it off, but none of the pocket's material is visible later.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Audio problem: The first time the man yells in "Frankendoodle", his mouth isn't in sync.
SpongeBob Meets the Strangler / Pranks a Lot - S3-E20
Continuity mistake: In Spongebob Meets The Strangler, the Tattletale Strangler's dots on his head change numbers constantly. Sometimes there are 5 on his right, sometimes 6, sometimes his left side has a scar and 5 dots, sometimes a scar and no dots.
The Great Snail Race / Mid-Life Crustacean - S3-E15
Continuity mistake: Gary crashes to a tire. After a while you see the tire is gone. Also, Gary stayed in the right of the track, crashed, but when SpongeBob helps him, Gary is in the middle of the track.
New Student Starfish / Clams - S3-E14
Continuity mistake: When Spongebob shows Patrick the good noodles chart all the stars are wildly scattered in each row. When Patrick is trying to announce his name to the class they're all in a neat row. When Mrs. Puff is removing the star from Spongebob's row they're scattered again.
Krab Borg / Rock-a-Bye Bivalve - S3-E8
Continuity mistake: In "Rock-a-Bye Bivalve," near the end, the timecard says it's midnight and it is dark outside. However, when the bivalve flies away, it's morning (judged by the shadows of the houses, even late morning), even though just a few minutes passed.
SpongeBob's House Party (aka Party Pooper Pants) - S3-E10
Continuity mistake: When Patchy the Pirate is flying through the houses, he finally hits a pole with nothing on him. Yet when Patchy comes screaming back into his hat, he had a broken window in him and wood through his hat.
The Great Snail Race / Mid-Life Crustacean - S3-E15
Continuity mistake: When Patrick and Squidward stick their heads through the windows of Spongebob's house, on the outside you can see that they're next to the front door. But from the inside, their heads are next to a totally different door.
Nasty Patty / The Idiot Box - S3-E4
Continuity mistake: When SpongeBob and Mr.Krabs are dragging the health inspector up the hill he doesn't have his hat on, but when he gets hit by the rock his hat is on.
Continuity mistake: Gary leaves big saliva trails. When Squidward realizes that Gary leaves these saliva trails, we can see that is a trail in front of Squidward's house. When Squidward tells SpongeBob about these trails in the language of the past, we can see that the trail of the saliva has changed: it bigger and almost in all the scenery. After a while, we see that the road goes directly to Squidward's house, to its door. How did the road change, if we haven't seen Gary moving?
Answer: I believe this is the Season 6 episode "Spongicus".