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.
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.
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.
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.