The High Life / Best Friends - S2-E10
Deliberate mistake: In "The High Life", there is a scene where Stinky submerges his head in a tank of water. He delivers the line, "Gee willickers, it's still ticking", and everyone somehow understands what he is saying with his head underwater.
Suggested correction: Nobody responds to what Stinky says, so there's no reason to assume that everyone understood him.
Girl Trouble / School Dance - S3-E18
Continuity mistake: Besides the fact that when Helga is sharpening her pencil, the desk arrangement changes, one of the students visible when she looks at Arnold is... Helga. This happens because the shot is taken from the episode "Helga's Love Potion."
Freeze Frame / Phoebe Cheats - S2-E8
Trivia: Arnold's computer is made by Purdy Electronics; Joseph Purdy wrote the episode.
Arnold's Hat/Stoop Kid - S1-E3
Question: Did Harold already know that the Stoop Kid had just left his stoop the first time? He would have known that a while ago due to a large crowd in the city or even in the newspaper.
Answer: No, he did not. He is seen getting off the bus with a suitcase, so he must have not been home for a few days so there is no way he could have known.