Bubblestand / Ripped Pants - S1-E1
Continuity mistake: When Spongebob first shows Patrick the technique for bubble-blowing, there are two red corals in the background - one on his right and one on his left. Later, when he shows Squidward the technique, the red coral on the left side of the screen disappears.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: Spongebob, controlled by Plankton, wasn't aiming directly at Squidward's house, but he eventually breaks through the wall.
Suggested correction: He might not have been aiming directly at Squidward's house at that moment, but after that shot, there is a 5-second shot of Squidward in his bed before SpongeBob crashes through his wall. Within those 5 seconds off-screen, there was time for Plankton (who is controlling SpongeBob) to turn SpongeBob towards the direction of Squidward's house.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In Plankton, when SpongeBob steps on Plankton, he steps on him with his left foot, except he pulls Plankton off of his right foot.