Continuity mistake: In "Fools in April", Squidward put some paper towels in his ears to block out the noise of Spongebob's laugh echoing throughout the Krusty Krab. He covers his ears, and in the next shot, the paper towels are missing and not in his hands.
Continuity mistake: In "Fools in April", Gary is sleeping next to his food bowl in the first shot, with Spongebob's bed nowhere to be seen. After hearing Spongebob's voice, Gary wakes up. In the next shot, Gary's food bowl is sitting in front of Spongebob's bed post.
Continuity mistake: In "Jellyfishing" when SpongeBob is playing Squidward's clarinet he says something like "Sorry my lips are a little moist" then he starts licking his lips. In a close-up shot of SpongeBob licking his lips, you can see that SpongeBob's arms are down, so where's the clarinet? In the next wide shot, SpongeBob is holding the clarinet again.
Revealing mistake: In "The Algae's Always Greener", Squidward walks in to the office to complain about SpongeBob's new rank. But when Squidward walks in, the krabby patties from the scene before are missing. Then after SpongeBob talks after Squidward complains, the krabby patties are back.
Continuity mistake: Plankton! When SpongeBob and Plankton are talking at night Plankton gives SpongeBob a golden spatula. When Plankton says he wants a Krabby Patty for his birthday SpongeBob drops it. Then when SpongeBob walks away, the spatula is nowhere to be seen.