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.
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.
Character mistake: In "I Heart Dancing", the lady at the Krusty Krab tells Spongebob the dancing audition is the next day. Later, Spongebob is practicing at Squidward's house for a whole night, and the next morning Squidward says they have one more day to practice, even though the audition should have been that day.
Plot hole: In "Mermaid man and Barnacle Boy", Plankton is shown as taller than the town at the end of the episode. However, when Spongebob is shrinking the people of Bikini Bottom, their sizes in the pickle jar seem to be equal with Plankton's actual height. In reality, Plankton should have been around the same size as the rest of Bikini Bottom's residence after the shrinking, not 5 times taller.
Continuity mistake: In the episode "Help Wanted" when Spongebob makes Krabby Patties for the anchovies, Spongebob chops lettuce, patties, and onions for some of the buns and the buns don't have patties, tomatoes, or cheese on them. And when he's done dancing, when you look at the patty buns there is no onion but there is a patty and lettuce. Also in later episodes, the way he made those patties isn't the way he makes them now. And the way he makes them now has tomatoes and cheese on them. But this could probably be wrong due to it being a pilot episode.
Continuity mistake: In "Where's Gary?" the length of the paddle ball string that SpongeBob uses seems to vary in certain shots. While the length is somewhat subjective one shot that is more conclusive is when Patrick finds Spongebob lying on the floor. The string on the paddle ball is fairly short. When the two get up to get a glass of milk, the string is now a lot longer.
Continuity mistake: In the episode 'Shell of a Man", when SpongeBob pushes over Mr. Krabs' shell off of the chair at Mr. Krabs' desk, you can see that there are 2 eye holes, a nose hole, and a very large hole for the mouth. But when SpongeBob puts the shell on, both his nose and mouth are in the large mouth hole, and his eyes are in the eye holes. But there is no nose hole.
Revealing mistake: In Club SpongeBob, when SpongeBob, Patrick and Squidward are in the forest, Squidward asks the magic conch shell if he can have something to eat. Straight after he asks "Can't you say anything else but 'No'?", it has a close-up of the shell. But Squidward's arm appears to be yellow, like SpongeBob's.