Other mistake: In the scene where Arnold meets the gang in the alley way, they give ideas to crash Rhonda's party. When Curly tells his idea to go to the zoo and free all the animals and there are shots of the gang looking at him confused,in two of the scenes, you'll notice that when Stinky and someone else looks at him, the background is at the school, not the alley.
Continuity mistake: In the Eugene's Bike episode, when Arnold has to tie his shoe, he sets his books down on a bike in a bike rack. This causes the bike to tip over and makes all the other bikes in the rack to fall down. Eugene's bike falls into the middle of the street and get ran over. When Eugene finds out his bike is destroyed, he looks at Arnold and yells. Right after this you get a good look at the bike rack. You'll notice there are no bikes in or around the bike rack.
Continuity mistake: In "Miss Perfect", Helga, Rhonda, Sheena, Phoebe, and Nadine are cooking up ways to make Lila's (the new girl) life miserable. In one shot, Rhonda is wearing her new blue outfit. When the scene cuts to the boys and Lila, and then back to the five girls, Rhonda is wearing her standard red sweater and black pants. For the rest of that day, she is back in her new outfit.
Continuity mistake: In "Oscar Gets a Job", Oscar goes around asking people for money. When he talks to Ernie, you can see that there is a phone and a light to the right of the door. When Arnold confronts Oscar in the hall, you can see Ernie's room (7). The phone has disappeared.