I agree with Cupid Kirby--if you look closely, you'll find all sorts of errors. But most you'll miss if you're just enjoying the show.
An arguably bona-fide goof:
In "I'm with Stupid," Patrick's "parents" (Janet and Marty, who aren't really his parents), say "Pats for Patrick," but since Patrick never tells them his name beforehand, how do they know his name is Patrick?
It's conceivable that they did know Patrick--only that they forgot that he wasn't their son (or maybe they saw his name written down somewhere in his rock?) Then again, when Patrick realizes near the end that they aren't his parents, he says "Who are you people?," in a way that suggests that they are strangers. But then again (paraphrasing Mermaidman in MMBB6), if there's one thing Patrick remembers, it's how to forget!
I saw that one recently, so I remembered that potential "goof" when I recalled this thread.
A couple more:
Near the end of "Pressure," Mr. Krabs says "Three cheers for feeling sorry for ourselves!" Then he says "hip-hip," and then everyone jumps up and says "hooray." The second time Mr. Krabs says "hip-hip," you see Squidward's lips moving, but you only hear Mr. Krabs' voice.
In "Club Spongebob," when Squidward is having that hilarious episode with the "magic conch shell," ("Can I have something to eat?" "No." "Can I have something to eat?" "No." "Can I have something to eat?" "No." "Can't you say anything else but 'no'?" "Try asking again." "Can I have something to eat?")
Then, the shell says "No," but in a different voice. In that quick scene, Squidward's hands are colored yellow.
In "The Camping Episode," Spongebob asks Squidward "Didn't you bring it [a can opener] when you hiked out here?" Squidward replies, "Why would I bother? We're ten feet from my house." Actually, that's not true--10 inches is probably the case.
The wikipedia articles on the episodes list some of these and many other goofs.