Club SpongeBob / My Pretty Seahorse - S3-E12
Continuity mistake: In "My Pretty Seahorse", Spongebob places a tray of Krabby Patties on the counter, which Mystery promptly eats, leaving an empty tray. In a few shots, the tray has disappeared from the counter.
The Snowball Effect / One Krabs Trash - S3-E3
Continuity mistake: Throughout the episode "The Snowball Effect" Patrick's house is missing.
Suggested correction: I just watched this episode and on at least two occasions I could see Patrick's home in the background.
Help Wanted / Reef Blowers / Tea at the Treedome - S1-E2
Continuity mistake: The office door in the Krusty Krab is missing throughout the episode.
Suggested correction: It's a pilot episode. Things can change with a show when it gets picked up into a series.
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."
Plot hole: After being spared, Medieval Sandy announced that she will help in the defeat of medieval Plankton. How did she know what they were planning?

Big Pink Loser / Bubble Buddy - S2-E3
Revealing mistake: Big Pink Loser: When Patrick is answering phone calls, the third time he picks up and says, "No, this is Patrick", the anchor symbol on his hat briefly vanishes. (00:04:36)
Suggested correction: This mistake can only be detected by freezing the film and advancing frame by frame. It is not visible while watching the film at a normal running speed. According to the rules of this site, this invalidates the error.
So, I reworded the mistake to say that it "briefly vanishes," because it's actually gone for a few frames, not one. I did not advance frame by frame to find the error. If you watch the scene at normal speed, it disappears for a brief moment, then comes back. I assume this correction might have been made without watching the scene, especially since the show was referred to as a "film."
This is not true. You can see it disappear if you watch it at normal speed; it does not require pausing at all. At least, I am able to see it.