Continuity mistake: When everybody comes to Squidward's house to persuade him to write a letter, you see that all the paper and pencils and bottles on the ground disappear.
Continuity mistake: In the morning when they all wonder where Santa is, and Spongebob keeps singing "Santa's coming tonight", once everybody walks away, Patrick appears right next to Spongebob.
Continuity mistake: When Spongebob is trying to get Squidward to write a letter outside, at the first shot of Spongebob, he's standing straight on the wood step thing, but the next shot he's facing to the side.
Continuity mistake: The picture that Squidward takes of Spongebob is different than what Spongebob is doing when he takes it.
Continuity mistake: In "Jellyfishing" when Squidward gets home from the hospital, Patrick exclaims Merry Christmas! However, later on in the series it is revealed that nobody in Bikini Bottom even knew what Christmas was.