Continuity mistake: At the beginning of "Mermaid Man and Barnacle Boy", when SpongeBob and Patrick are watching TV viewing Mermaid Man and Barnacle Boy show, you can see that these heroes have 5 fingers on their hands, as the real human beings. However, when SpongeBob and Patrick meet these heroes, as in the rest of the show, you can see that now, the heroes, have 4 fingers on their hands, as cartoon characters usually have.
Continuity mistake: In "Neptune's Spatula", Patrick takes a picture of SpongeBob holding the spatula. When this happens, we can see that SpongeBob is a little worried because clouds have appeared there. However, after a while, Patrick shows the picture to Neptune, and we can see that in the picture SpongeBob is smiling and pointing with the spatula.
Continuity mistake: In the episode Welcome to the Chum Bucket, when Plankton is reading a story to SpongeBob, he is interrupted. When he looks up and sees SpongeBob asleep, Sponge doesn't have his Chum Bucket Bucket Helmet on. When Plankton decides not to hit SpongeBob with a mallet and wakes him up, Sponge has the helmet on again.