You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Deliberate mistake: Spongebob gets stuck in the top of a tree as Gary removes the ladder. In previous episodes it's quite clear that he's more than willing to 'fall' as he takes no damage when hitting the ground due to the low fall speed.
Bummer Vacation/Wigstruck - S4-E14
Deliberate mistake: When SpongeBob is playing with his Krusty Krab action figures, their faces change expressions instantly.
Suggested correction: This is simply one of the many gags that occur in this show. In the same scene, SpongeBob has a third arm while playing with the action figures. Problematic? No, that's a gag too. Throughout the show, the characters are capable of doing many impossible tasks (drinking water underwater, floating, growing limbs, etc.). The expressions on the action figures changing is another one of the impossible things that can happen in this fantasy world.
Grandma's Kisses / Squidville - S2-E9
Deliberate mistake: Spongebob and Patrick sucks the windows off Squidward's house using leafblowers. The holes in the wall that the windows were in magically disappear.
Roller Cowards / Bucket Sweet Bucket - S5-E8
Deliberate mistake: In 'Bucket Sweet Bucket' there's no way that Plankton managed to reach with his paint brush to repaint the entire front of his establishment from the top of Squidward's head.
