The episode Girl Trouble had two slip-ups. The first one is Helga gets up to sharpen her pencil and as she is sharping it, they show a shot of the Arnold sitting at his desk where you can clearly see Helga sitting behind him. At first I thought that the pencil sharpener might have been in back of Arnold's desk, but it isn't. This was definitely a slip-up.

The second is more an easter egg rather than a slip up. Earlier in the episode, when Arnold's grandpa is telling him a story, if you pay attention to the shelf in the background you'll notice that there are small figures of Arnold and Gerald on the bottom shelf.