Other mistake: In the one scene, Mr. Krabs and Plankton notice Stinky Burgers was shut down. When it cuts to their reactions, Mr. Krabs' eyebrows are missing.

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: After Patrick bites his finger while eating the cookie, his shorts are not fully coloured in at the bottom of the screen, but they instantly are once Grandma kisses his finger. (00:08:37)

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: After Patrick sucks all of Grandma's cookies into his mouth like a vacuum, as the cookie rolls towards SpongeBob, his lower body is missing, then it appears once he moves. (00:07:44)

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: After Patrick sucks all of Grandma's cookies into his mouth like a vacuum, a cookie rolls towards SpongeBob, and as he says, "It appears to be my lunch hour," a watch appears on his left wrist mid-shot, then disappears. (00:07:49)
Grandma's Kisses / Squidville - S2-E9
Continuity mistake: Grandma's Kisses: Throughout the scene where SpongeBob and Patrick are in Grandma's kitchen, the plate of cookies repeatedly vanishes from the table. (00:07:03)

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: When SpongeBob goes to his grandma's house with Patrick, Grandma tells him to give her a kiss, and in the next shot of SpongeBob, his right leg is missing. (00:05:13)
Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: When SpongeBob is having his "mature conversation with Patrick," he tells him, "We are supposed to be adults!" In the next shot, when the camera moves over to Patrick, SpongeBob's right hand stays visible on screen; then it vanishes mid-shot. (00:06:46)

Grandma's Kisses / Squidville - S2-E9
Continuity mistake: Grandma's Kisses: When SpongeBob goes to have a "mature conversation with Patrick" in the kitchen, Patrick holds a glass of milk in his hand. SpongeBob then says, "We are supposed to be adults!" and in the next shot, the glass of milk suddenly appears on the table. (00:06:44)

Grandma's Kisses / Squidville - S2-E9
Continuity mistake: Grandma's Kisses: At the end, Grandma gives SpongeBob his sideburns and a cookie. He holds the cookie in his right hand, but in the next shot, the cookie has vanished from his hand. (00:12:00)

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: After Grandma pulls the plug from the floor, she kisses SpongeBob and says that he can kiss his Grandma and still be an adult. In this shot, SpongeBob's legs are completely missing. His pant legs also vanish and reappear mid-shot, and even his legs appear for a frame or two, then vanish. (00:11:48)

Grandma's Kisses / Squidville - S2-E9
Other mistake: Grandma's Kisses: When SpongeBob goes to his Grandma's house with Patrick, Grandma tries to kiss SpongeBob, but SpongeBob's reflection in Grandma's glasses is not reversed; note the holes on his face. (00:05:14)
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Plankton! When Plankton pulls out a radio player to play his evil music on SpongeBobs pillow, it has disappeared when Spongebob wakes up. SpongeBob didn't move on it.
The Secret Box / Band Geeks - S2-E14
Audio problem: At the end of "Band Geeks" when everyone is playing "Sweet Victory" at one point Mrs. Puff is shown playing the guitar. When this happens, you can see the others in the background not doing anything, even though their instruments are heard.
Procrastination / I'm With Stupid - S2-E19
Continuity mistake: In "Procrastination" when Spongebob is moving back and forth on his chair while writing his essay there is no pencil on the desk, but when he goes back to work on the essay there is.
Suggested correction: The pencil is sitting to the right of the paper the entire time. It's hard to notice at first, but it's there.

Best Day Ever/The Gift of Gum - S4-E20
Revealing mistake: When Squidward says "I suppose if you haven't fixed my clarinet, the concert would have been a bust", Sandy's tail is the same color as her suit.
SpongeBob Meets the Strangler / Pranks a Lot - S3-E20
Plot hole: In "Pranks A Lot", Patrick and SpongeBob scare Sandy. When Sandy runs, gets into her rocket and flies away. When she moved bubbles appeared meaning there's water in her tree house. There's no water in there in other episodes because she's a land animal and breathes air.
SpongeBob Meets the Strangler / Pranks a Lot - S3-E20
Plot hole: When the invisible Spongebob and Patrick scare Sandy, they are using a sheet to appear as "ghosts". However, the form of the sheet reveals that they don't have their helmet bowls on. How could they survive in the treedome that time? They sounded fine, not dehydrated.

Revealing mistake: In "Not Normal" when SpongeBob says "Hmm. This video tape should help," his left arm is missing. (00:01:25)
You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Audio problem: In the beginning of "Shanghaied" during the Patchy the Pirate segment, Patchy says, "Roll the cartoon" but his mouth obviously says something else.
Plot hole: In "Once Bitten", Mr. Krabs never unlocks the doors to the Krusty Krab, but at the end of the episode, Squidward enters with no problem.
Suggested correction: Maybe Squidward has a key to the Krusty Krab that Mr. Krabs doesn't know about.
He could still have a key, but we don't see it.
Whether or not Squidward owns a key to the Krusty Krab is beyond the point of the mistake here. The point is that Squidward is able to walk into the Krusty Krab despite the doors being locked, and he doesn't use a key or anything else to unlock them. He just pushes them open.
Maybe the doors were not locked properly.