Continuity mistake: In "Sleepy Time", Spongebob is driving a car in his dream. When he starts to drive faster, he sticks his tongue out on his left cheek. When he makes a left turn in the next shot, it's sticking out on the right cheek.
Jellyfishing / Plankton! - S1-E3
Continuity mistake: Plankton! When SpongeBob and Plankton are talking at night Plankton gives SpongeBob a golden spatula. When Plankton says he wants a Krabby Patty for his birthday SpongeBob drops it. Then when SpongeBob walks away, the spatula is nowhere to be seen.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Tea at the Treedome", in one shot, Spongebob's pants are inflated, and in the next shot they're not.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: In the episode "Pickles", there is a large fish named Bubble Bass. Although his name is Bubble Bass, the captions say his name is Bubble Bath. It is clear that Spongebob is saying "Bass" not "Bath", and his name is given as Bubble Bass in SpongeBob's Diner Dash.
MuscleBob BuffPants / Squidward, the Unfriendly Ghost - S1-E11
Continuity mistake: When Patrick throws Squidward the watermelon, it lands on his torso and he falls down. When the camera goes back to Squidward, the watermelon is in his mouth.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: In "Help Wanted" Gary doesn't have eyelashes. In every other episode he does.
Suggested correction: So Gary not having eyelashes could count as an early design for him. It's common that characters and environments may undergo changes after a pilot. Not a mistake.
But Gary never had eyelashes.
Texas / Walking Small - S1-E18
Continuity mistake: In "Walking Small", The eel that stole Spongebob's ice cream cone throws it at his face. Different shots some show ice cream on Spongebob's nose, and some show that Spongebob's face is clean.
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: When Spongebob is cutting his Jack-O-Lantern, he cuts out an eye on his right, but in the shot from inside the pumpkin the eye hole is gone, then the eye reappears.
Continuity mistake: Rock Bottom: When the cardboard version of Spongebob next to the candy machine is shown, it is frowning, but it turns into a smile when it falls over. (00:18:48)
Continuity mistake: Rock Bottom: After SpongeBob and Patrick enter the bus, when SpongeBob asks Patrick if he has any change and for the duration of this shot, both the gear shift on the floor beside the driver and the open door of the bus have vanished, then they reappear.
Hooky / Mermaid Man and Barnacle Boy II - S1-E20
Continuity mistake: Hooky: When SpongeBob is hooked the pointy tip of the hook is facing out, but when he asks Krabs what he should do, the hook is hooked into SpongeBob's pants the opposite way, with the pointy tip facing him. Additionally, he's hooked at the back of his underwear and pants, but when Squidward is holding the fishing pole the hook is at the front of the underwear, which are also perfectly intact despite being ripped off SpongeBob.
Fools in April / Neptune's Spatula - S1-E19
Continuity mistake: Fools in April: While Squidward is having difficulty apologizing to SpongeBob, they're both standing in front of the pineapple with its front door wide open inward, but when Squidward places the bubble over his head the front door is suddenly wide open outward, so Squidward could slam the door.
Valentine's Day / The Paper - S1-E16
Continuity mistake: The Paper: The front door of Squidward's house repeatedly switches between opening at the right side and opening at the left side, and the round door knob also changes to a door handle as well, but then reverts back to the round knob.
SB-129 / Karate Choppers - S1-E14
Continuity mistake: SB-129: When Squidward opens the door to the time machine, the exterior side of the door has a handle at the left side and opens at the left, but the interior side of that door also has the handle at the left side, though it should be at the right side. Then when Squidward activates the machine, the exterior handle is now at the right side and it opens at the right.
Nature Pants / Opposite Day - S1-E9
Continuity mistake: Opposite Day: The front door knob on Squidward's house repeatedly switches between the left and right side of the door, so it opens the opposite way (it has nothing to do with it being opposite day).
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: Mermaid Man wears green tights, but after SpongeBob absorbs the water ball like "some kind of evil sponge," when Mermaid Man and Barnacle Boy start doing the dog paddle, Mermaid Man's tights have vanished in this shot.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When Barnacle Boy opens the box with the two rings inside, in the closeup the "B" ring is on the left and the "M" ring on the right, but in the wideshot Barnacle Boy removes the ring on the left (the "B") and places it on Mermaid Man's finger, then in the next shot we see it's the "M" ring, before both rings vanish.
Mermaid Man and Barnacle Boy / Pickles - S1-E6
Continuity mistake: Mermaid Man and Barnacle Boy: When SpongeBob and Patrick (dressed in their superhero costumes) exit the pineapple the front door opens at the right side (outward), but after getting on Squidward's nerves, when they retreat back inside the front door opens the opposite way at the left side (inward).
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: Spongebob's belt is missing when his clothes are first revealed while dangling in midair.
Scaredy Pants / I Was a Teen-age Gary - S1-E13
Continuity mistake: The Krusty Krab is filled with Halloween decorations during the episode, but when Spongebob jumps to hide in a barrel there are no decorations in sight.