Continuity mistake: Plankton's Army (aka Plankton's Last Stand) / Missing Identity: When the screen splits into 4, the last 2 events are not in chronological order. That is, they are not in the same order as they always have been.
Continuity mistake: The Krusty Krab kitchen sometimes has deep fryers, and sometimes it doesn't. When it does, the fryers change locations in the room between episodes.
Other mistake: In "SpongeBob and the Clash of Triton," the title card says it is called "Neptune's Party," thus making it a wrong title.
Suggested correction: "Neptune's Party" was the original title for "The Clash of Triton."
Continuity mistake: Sometimes there is a window on the right side of Squidward's house, sometimes there's not.
Continuity mistake: In some episodes, Spongebob can't even lift marshmallows on a stick (Ripped Pants). However in Texas, he somehow flips a guy coming up behind him.
Continuity mistake: If you look carefully, you will notice that on the title sequence, patchy the pirate's eyepatch changes eyes. This varies from episode to episode.
Suggested correction: The eyepatch doesn't change position from episode to episode. You must be thinking of "Christmas Who?" where Patchy accidentally hits himself in the eye with his hook. And the pirate from the theme song's name is Painty the Pirate. Patchy and Painty are two completely different characters.
Revealing mistake: In "Patrick! The Game," when Squidward holds out the notepad, it's obviously written on. Just when the bubble transition comes, the notepad and all the other papers on the floor clear themselves.
Continuity mistake: Throughout the whole episode of "Missing Identity", SpongeBob's shirt is backwards. This is seen with his sleeves being supposedly behind him. The sleeves are missing from the front, which is normal, but throughout the episode, pay attention to behind SpongeBob. His sleeves are supposed to be behind him, but are missing altogether.
Other mistake: Always in the older episodes (and sometimes in the newer ones), when a fish in the background takes his/her second bite of a sandwich, the sandwich still looks like the first mark. It does this on every bite after the first.
Continuity mistake: In "The Krusty Drive-through", Mr. Krabs creates a drive-through. However, an updated one can be seen in older episodes.
Continuity mistake: In the episode "The Sewers of Bikini Bottom", Mr. Krabs is talking to the owners of the Krusty Krab Stadium and there are two pennants on the wall behind them. In a later shot through a window, there is only one pennant on the wall.
Continuity mistake: In "Patrick! The Game", the whole group is outside and Squidward rolls a die. The die disappears in the next shot.
Continuity mistake: In the episode "Patrick! The Game", Patrick puts on a surgeon mask. This mask eventually disappears in a later shot.
Continuity mistake: In "Patrick! The Game", Spongebob takes the rulebook and puts it off to the side. In the next shot, the book disappears.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: In "Bubblestand" after Squidward blows the huge bubble, he tells Spongebob and Patrick that the ability to blow bubbles is in his genes. If you look at the position of the bubblestand sign, the sign is facing the direction Squidward is talking. The sign had always been facing the street, which means that Squidward was actually talking towards the street, when Spongebob and Patrick are actually to his right.
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.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: In the scene where Squidward complains to Spongebob about the construction noise from his stand, Squidward's porthole in the background is black, but from the interior there is a light on (Note: this also happens in every other shot of his house.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: SpongeBob takes off his ripped pants, and throws them on the ground. His shirt sleeves are perfectly intact. Next, Sandy and Larry are shown playing volleyball. When SpongeBob is shown again, his pants are still gone, and so are his shirt sleeves.
Bubblestand / Ripped Pants - S1-E1
Revealing mistake: In "Ripped Pants", Spongebob plays the guitar and chord changes are heard, but his fingers on the neck of the guitar do not move.
Bubblestand / Ripped Pants - S1-E1
Continuity mistake: In "Ripped Pants", we see 3 other people at the square lifting weights besides Sandy. When Sandy lifts her weights, the crowd cheers, and we get a wide shot of the square, we see that the 3 thugs are gone.