Deliberate mistake: When the world is counting down to the new year, we see people in various countries, Egypt, the USA etc all counting down together. Because of time zone differences this isn't possible. [It is a little joke.] (00:01:35)
Yug Ylimaf - S11-E4
Deliberate mistake: The time machine reverting causes everything in life to go backwards. However, although the characters' actions are reversed, their dialogue is always spoken forwards and not backwards. (00:08:00)
You Wish ('Shanghaied') / Gary Takes A Bath - S2-E11
Deliberate mistake: Spongebob gets stuck in the top of a tree as Gary removes the ladder. In previous episodes it's quite clear that he's more than willing to 'fall' as he takes no damage when hitting the ground due to the low fall speed.
Deliberate mistake: At the very end, Tommy And Merton discover the video tape which contain pictures of Merton that had been film by her sister Beckie, but the movie was filmed and the time ''rewind'' because of the spell. So in reality, the movie was never filmed.