Continuity mistake: In "Valentine's Day", SpongeBob and Patrick arrive at the fair. They watch the fair. Patrick says "You bought me a fair?", and Patrick runs to the fair. When he starts saying, "Get out of my fair.", we see that SpongeBob is closer to the fair than he was before.
Continuity mistake: In "No Free Rides", when Spongebob and Mrs. Puff are fighting in the car, they eventually go over a cliff. We see a view of a police car under them, next to the cliff and a billboard. We also see a shot of the police car facing a hill or two. The car flies out of nowhere onto the police car, from behind a hill, not off the cliff. The landscape in the scene changes in each shot.
Continuity mistake: In The Smoking Peanut, after Spongebob sees Sandy he runs home. When he's trying to open the door if you look to the right the ground is completely flat and has nothing in it. Yet when Patrick comes, while he is saying, "I followed these footprints to this exact spot", there are footprints.
Continuity mistake: When Spongebob and Patrick have run away, when they are fighting about the chocolate, Patrick has chocolate all over his mouth. Patrick says something like "I'll get there first" and starts running after Spongebob, and in the next shot his face is completely clean.
Continuity mistake: When his pants fall off when he's trying to hide, his pants are hooked to the plant by the brown part of his pants, but when Sandy comes looking and she sees his pants on the plant, they're hooked by the white part.
Continuity mistake: When Spongebob goes to answer his door, Patrick was obviously in front of the door. After Patrick says, "Spongebob doesn't like me anymore", it cuts to a different shot to show the outside of the front door, and Patrick has moved to the side of the door.