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.
Suggested correction: The episodes are not always meant to be in chronological order. It's entirely possible that "Christmas Who?" took place before "Jellyfishing."