Fools in April / Neptune's Spatula - S1-E19
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.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Tea At The Treedome" Patrick is seen lying on his rock, and the wooden stem thingy on his house is to the right of his house instead of the middle, and is a lot taller too.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: In "Jellyfishing" when SpongeBob is playing Squidward's clarinet he says "Sorry, my lips are a little dry." Then he starts licking his lips. In one shot, the clarinet disappears from SpongeBob's hands. Then it reappears in the next shot.
SB-129 / Karate Choppers - S1-E14
Continuity mistake: In "Karate Choppers" when SpongeBob sticks his arm through Sandy's phone, Sandy sticks SpongeBob's hand through the other end, then Sandy puts the phone down and SpongeBob's hand immediately disappears.
Continuity mistake: When SpongeBob sees the kandy machine, the front of the machine is facing the road, but when he runs over to it, the front is now turned away from the road.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: The office door in the Krusty Krab is missing throughout the episode.
Suggested correction: It's a pilot episode. Things can change with a show when it gets picked up into a series.
Continuity mistake: When SpongeBob and Patrick see the map, a compass is seen next to it. As the two start touching the map, the compass has disappeared.
Culture Shock / F.U.N. - S1-E10
Continuity mistake: When we first see Squidward in the canyon background, his outlining is gone. Then, in the next shot, it's back.
Culture Shock / F.U.N. - S1-E10
Continuity mistake: In "F.U.N.", Mr. Krabs sets down the Krabby Patty in front of Plankton. Almost the whole plate is on the yellow part of the table, but when the camera cuts to Plankton, the plate is mostly in the red part of the table. In the next shot, the plate returns to its original position.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: In "Fools in April", Spongebob is scrubbing the floor and a customer comes up to him to ask for a couple of ice cubes. In the next shot, the water puddle on the floor gets increasingly bigger.