In the episode Jellyfishing, Squidward was holding the net in his left hand. When he was catching a jellyfish, the net was in his right hand. When he was chased by a huge jellyfish, the net was back in his left hand.
In the SpongeBob Christmas Special, Patchy the Pirate's hook hand changes sides between scenes. This is part of the humor of Patchy; he's an obviously fake pirate played for laughs. He is shown switching his eye patch from eye to eye as well; just like both of his eyes are perfectly fine, he doesn't need a hook, and only has one to look like a pirate.
In the episode where Spongebob is making his own Mermaidman movie, it is said that Patrick kept the lens cap on during the entire film, but, you can easily see that that is not true, since you see the camera filming without a lens cap.