Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: Mermaid Man and Barnacle Boy IV: When SpongeBob runs into the kitchen with Mermaid Man's secret utility belt, the door swings open facing away from the grill, but when Squidward demands to know what's going on in the kitchen, the door opens the opposite way.
Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: In "Doing Time", Spongebob's entire face fills the chili bucket, but when he peeks out, his body is relatively smaller than the bucket.
Mermaid Man and Barnacle Boy IV / Doing Time - S3-E1
Continuity mistake: When SpongeBob zaps the pickles, he is standing next to the door. He instantly moves to the center of the room in a subsequent shot.

Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: Frankendoodle: When SpongeBob pranks Squidward by pulling the dollar away from him, Squidward's monocle falls on the ground, but when the mustache flies away, the monocle has vanished. A chain on the monocle also appears in one shot, then disappears. (00:15:47)

Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: Frankendoodle: When DoodleBob first starts beating up Squidward, the door to Squidward's house is open, but two shots later, the door has completely vanished. (00:16:32)
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: In the episode Welcome to the Chum Bucket, when Plankton is reading a story to SpongeBob, he is interrupted. When he looks up and sees SpongeBob asleep, Sponge doesn't have his Chum Bucket Bucket Helmet on. When Plankton decides not to hit SpongeBob with a mallet and wakes him up, Sponge has the helmet on again.
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.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: In 'Welcome to the Chum Bucket', the sky is constantly changing in an abnormal way. First, it is daylight when Plankton takes Spongebob into the Chum Bucket. When Spongebob starts singing, the sun is either coming up or going down. When Mr. Krabs starts singing, look through the hole in the wall and the sky looks to be about afternoon. When Spongebob and Mr. Krabs finish their song, it's nighttime.
Welcome to the Chum Bucket / Frankendoodle - S3-E2
Continuity mistake: The pencil's length in 'Frankendoodle' varies in between above and beneath the water surface.
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.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In "One Krab's Trash," after SpongeBob discovers the drinking hat at Mr. Krabs' yard sale, the two straws are connected to a cylinder with a hole. But when Mr. Krabs says "You were born to wear this hat!" the little cylinder has vanished. Later when SpongeBob is blowing bubbles, the cylinder has reappeared. (00:02:25 - 00:05:00)
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: On "One Krab's Trash", when Mr. Krabs draws a ghost on a sheet of paper, it shows before it goes into Spongebob's rooms that there's only writing on one side (i.e. the ghost) and when it goes into his room, a shopping list is on the back.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In One Krabs Trash, Spongebob pays Mr. Krabs with what looks like two dollars, which should have been five, and when he comes back he has two dollars that doubles into four in the next shot of him leaving.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In the scene where, Squidward accidentally squirts lemon juice in his eye it goes in his right eye but he squints with his left eye.
Suggested correction: In "The Snowball Effect", Squidward squirts the lemon wedge's juice into his left eye and he closes his left eye. There is no continuity error.
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.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In The Snowball Effect, Squidward builds his fort between his and Spongebob's house later in the ending scene his fort has moved about 30 yards away.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: In "Snowball Effect" when Squidward rips apart the "peace treaty" it is nothing but shreds on the ground. About ten shots later, the shreds disappear.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: Throughout the episode "The Snowball Effect" Patrick's house is missing.
Suggested correction: I just watched this episode and on at least two occasions I could see Patrick's home in the background.
Nasty Patty / The Idiot Box - S3-E4
Continuity mistake: In the scene where Spongebob and Mr. Krabs bury the health inspector, Spongebob buries him so that way his head is above ground covered by a pile of dirt. In the next shot of the buried health inspector, he is buried horizontally.