
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.
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.
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.

Sid the Vampire Slayer / Big Sis - S5-E3
Other mistake: Sid the Vampire Slayer: While Sid stands in front of the mirror and points his rubber sword at Arnold and Stinky, the two ghoulish vampires, Arnold asks him, "How can we be vampires if we have reflections?" So when Sid is aware of his mistake, Arnold's eyes disappear and reappear in his reflection mid-shot.

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Helga Blabs It All: When the boys get ice cream from the Jolly Olly ice cream truck, Arnold gets a chocolate popsicle, and Gerald gets an ice cream cone. Then, when Helga falls into Arnold's attic bedroom, all the boys stare at her, and as Helga backs out of the room, the ice cream cone Gerald holds changes to a chocolate popsicle.

Save The Tree / New Teacher - S2-E1
Continuity mistake: New Teacher: Arnold's classroom door vanishes from its door frame in various shots, then the door reappears in its proper place. That door's doorknob also switches between the right side of the door and the left side a few times.

Arnold Betrays Iggy / Helga and the Nanny - S3-E10
Continuity mistake: Arnold Betrays Iggy: When Arnold goes to Iggy's home near the start, the front doorknob is on the left side of the door, but the next time Arnold goes to see Iggy to bring him the box of chocolates, the front door opens the opposite way, with its doorknob now on the right side of the door. (00:01:20 - 00:06:40)

Parents Day - S5-E6
Continuity mistake: During the flashback, when little Arnold says goodbye to his parents, in the next shot of Stella and Miles, the bag's strap is slung over his dad's left shoulder as a crossbody, but mid-shot, the strap switches to his right shoulder with the bag on the opposite side. (00:14:30)

Parents Day - S5-E6
Continuity mistake: When Grandpa enters and exits Arnold's bedroom, the door opens the opposite way in various shots, with the doorknob on either the left or right. Additionally, the light switch beside the door appears and disappears, between shots.

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Helga Blabs It All: While Helga hides in the overhead ventilation shaft, the vent cover has either four, five, or six slat openings in various shots.

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Helga Blabs It All: When Helga falls from the vent opening, she knocks the telephone and answering machine onto the floor. Just as Helga notices the tape in the answering machine, the push button telephone has changed to a phone with a rotary dial. It then changes back to push button. (00:10:05)

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Harold the Butcher: At Mr. Green's meat store, there are at least two instances that the word "MEATS" is misspelled as "MAETS" on the store's aprons. When Mr. Green gives Arnold the package for Grandma, Green's apron changes to the misspelling. Then, when Harold returns to help Green with the crowd of customers, Harold's apron has the misspelling.

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Harold the Butcher: After Mr. Green informs Harold that his week is up, Harold follows Mr. Green into the store, and the green front door remains open. Mr. Green explains that he's getting ready for the annual meat sale, and as Harold begs to keep working in the store, we can see in the background that the store's green front door has vanished. The open green front door is back when Harold exits the store. (00:19:05)

Helga Blabs It All / Harold the Butcher - S3-E1
Continuity mistake: Helga Blabs It All: While Helga is in the ventilation shaft, when she calls Phoebe for help, the rope is tied around Helga's waist with a knot at the front, but it cuts to a closer shot and the knot vanishes.

Helga's Masquerade / Mr. Green Runs - S5-E2
Other mistake: Mr. Green Runs: When Green tells Arnold he can't be himself and needs to come up with some fancy words, Arnold is wearing a "Vote Green" button. Then, just as Green says, "I gotta get outta here," Arnold's button now reads "Voet Green" with Vote misspelled.

Part-Time Friends / Bio Square - S2-E19
Continuity mistake: Part-Time Friends: When Arnold and Gerald get part-time jobs at the flower shop, while Mrs. Vitello explains things to them, she asks if she's going too fast, and in the next close-up, Arnold's apron vanishes, then it reappears.

Part-Time Friends / Bio Square - S2-E19
Other mistake: Bio Square: While Phoebe and Stinky are telling the class about their science fair experiment, just as Phoebe shares that it was in honor of her hero, "I.P. Pavlov," watch as Stinky's eyes move off to the side of his head, then return to normal.

Casa Paradiso / Gerald's Tonsils - S3-E3
Continuity mistake: Gerald's doctor's name is spelled "Murray Stieglitz" on the sign, but "Steiglitz" in the credits.

Weird Cousin / Baby Oskar - S4-E11
Continuity mistake: In "Baby Oskar" when Suzie answers the phone there are 12 buttons on the phone, but when she is sitting on the bed there are 9 buttons.

Helga's Show / The Flood - S3-E15
Continuity mistake: Grandpa's rubber raft got much bigger between the time he left the greenhouse and the time he arrived.

Big Gino / Jamie O. In Love - S4-E2
Other mistake: In the cafe, after Charice speaks, when Gerald says "Aloha, Gladiators on Ice", there are three places where Gerald's mouth disappears.

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.