The Little Pink Book/Field Trip - S1-E2
Continuity mistake: On the "Presidents of the United States" sign behind Helga, the word "United" becomes "Nvited"
Operation Ruthless/The Vacant Lot - S1-E7
Continuity mistake: In Operation Ruthless, the pedal in Helga & Phoebe's bumper car changes color from black to gray to black between shots.
Helga's Makeover/The Old Building - S1-E4
Continuity mistake: When the classroom is first shown, the first two desks against the wall near the door are occupied by Curly and Eugene, Gerald and Arnold are sitting where Curly and Eugene were shown.
Tutoring Torvald / Gerald Comes Over - S1-E13
Continuity mistake: Arnold switches from his left hand to his right hand when taking the test.
Suggested correction: I don't believe it is ever established whether Arnold is left or right-handed in the series. Without confirmation; he may very well be part of the ambidextrous population that uses both. I used to write with both hands myself in school.
Except the mistake is saying he switches hands in between shots during the test. Not that one episode he's left handed and the next he's right handed. Yes, the teacher was shown for about 1-2 seconds before the switch happened. But these mistakes should be considered valid as an actual mistake in animation rather than to suggest to the audience that for no reason whatsoever, Arnold switches hands to finish the test, and only does so when not seen.
I'm ambidextrous myself, and I often switched hands when taking tests. It was very useful for preventing hand cramps. It only takes a couple of seconds to switch the pencil to the other hand, so I don't see why Arnold can't do it within that span of time too.
I do believe he is ambidextrous. In "The longest Monday" he is using chop sticks with his right hand. Many other episodes he uses his left hand to write.
Tutoring Torvald / Gerald Comes Over - S1-E13
Continuity mistake: Arnold and Gerald have to climb stairs to get to Oskar's apartment, but this would mean the building has three floors, and the outside views indicate that there are only two (plus the attic).
Arnold's Hat/Stoop Kid - S1-E3
Continuity mistake: When Grandpa is telling Arnold about how how he tried to cover his head when his hair falls out, the camera cuts back to him with his arm on Arnold's shoulder and Arnold has his hat on, even though the whole story is about him losing his hat.
6th Grade Girls/The Baseball - S1-E5
Continuity mistake: While walking down the stairs, Maria only has three toes on each foot; she has four at the pool.
Benchwarmer / Cool Jerk - S1-E11
Continuity mistake: The scoreboard has room for 10 names on each side when shown in close-up, but when Arnold is shooting free throws, there are only 7 spaces on each side.
Downtown as Fruits / Eugene's Bike - S1-E1
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.
Magic Show / 24 Hours to Live - S1-E18
Continuity mistake: The boarding house has a downstairs bathroom, but in "Gerald Comes Over", there's only one bathroom and it's upstairs.
False Alarm / World Records - S1-E17
Continuity mistake: In "World Records", during Arnold's inspirational speech on the stoop of the boarding house, Gerald is sitting on the railing. He changes positions from sitting facing Arnold on the steps to facing the street between shots.
Olga Comes Home / Sally's Comet - S1-E15
Continuity mistake: In Sally's Comet when Gerald, Arnold, and Grandpa are in the traffic jam on the way to Hawk Mountain the position and type of cars around them change. When we first see the car there is a truck there and no room for them to turn around. When they do turn around then there is room and the truck is gone.
Tutoring Torvald / Gerald Comes Over - S1-E13
Continuity mistake: In Gerald Comes Over, Gerald says whenever he goes to Arnold's house he always goes straight to Arnold's room and has never seen all of Arnold's house. Also he seems never to have met any one else that lives there, but in previous episodes we have seen him in other parts of Arnold's house and met many of the people that live there.
Suggested correction: Other than the few episodes that take place at a certain time; this series is not meant to be taken in chronological order. Just roughly during the same 4th grade school year.
Continuity mistake: When Helga is talking about Arnold, the computer store she is in front of is on a corner (Phoebe is seen going around the corner) but a few shots later the store is no longer on a corner.
The List/Haunted Train - S1-E8
Continuity mistake: At the beginning of The Haunted Train Grandpa's ice cream changes color from orange to white.