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.
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.
Other mistake: Mugged: When Arnold gets mugged, some of the shots use a flipped background. Note the wall colours, and the sign that says "MARKET," which is reversed. (00:01:16)
Other mistake: Mugged: When the people are standing outside Sunset Arms waiting for Arnold to come out of the garage, Oskar is coloured incorrectly: he has grey hair, a grey beard, an orange shirt, a light blue jacket, and white shoes. (00:05:12)
Continuity mistake: Mugged: Throughout the scene with Arnold and Grandma on the bus, Arnold is not wearing his hat. When the creep runs off the bus and the camera shows Arnold and Grandma from outside the bus, Arnold is wearing his hat. (00:11:35)
Door #16 / Arnold as Cupid - S1-E10
Other mistake: Arnold as Cupid: When Oskar gives Arnold breakfast, besides the fact that the objects move from the left side of the tray to the right between shots, look at the glass of orange juice as Oskar lowers the tray to Arnold. Despite Oskar never rotating the tray around, the glass of orange juice glides itself over to the top left corner of the tray. Very weird. (00:14:34)
Door #16 / Arnold as Cupid - S1-E10
Audio problem: At the hat store, when Arnold says "Huh? What are you, nuts?", his lips don't move - but Gerald's do.
Door #16 / Arnold as Cupid - S1-E10
Factual error: Ernie removes two screws from a glass panel in the skylight, but then lifts the panel from the side that's still screwed in.
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.
Benchwarmer / Cool Jerk - S1-E11
Other mistake: The names for the Green and Yellow teams' players are the same.
Das Subway / Wheezin' Ed - S1-E12
Factual error: There's no way Grandma could have connected two "live" wires with her bare hands without electrocuting herself, and there's certainly no way the wires could have stayed connected.
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.
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).
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.
Abner Come Home / The Sewer King - S1-E16
Continuity mistake: Abner Comes Home: When Abner comes back to the boarding house at the end, Arnold starts running towards him, and there is no mud puddle. In the next few shots, a mud puddle suddenly appears for both of them to fall into and roll in. Then in the next wide shot, the mud puddle disappears, and in the last two shots of the episode, it returns once again. (00:11:09 - 00:11:48)
Abner Come Home / The Sewer King - S1-E16
Continuity mistake: Abner Comes Home: Some of the objects and other things in the Sunset Arms backyard disappear, reappear, change, or move around in various shots. (00:11:27)
Abner Come Home / The Sewer King - S1-E16
Audio problem: When Arnold is playing chess with the Sewer King, Arnold jumps across the table and knocks the King over. This sequence appears to be sped up: the toilet crashes way after it is destroyed, and the King says "Noooooooooooo," yet his mouth never moves.
Suggested correction: The Sewer King's mouth does move, but it does say the line a little too late. However, the toilet crashing sound is exactly where it should be, and the scene is definitely not sped up.
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.
Magic Show / 24 Hours to Live - S1-E18
Audio problem: Magic Show: During Arnold's magic show, the kids start chanting, "Make Helga disappear!" When Helga says, "Alright you bunch of clods," they stop, but their voices can still briefly be heard. (00:03:28)
Magic Show / 24 Hours to Live - S1-E18
Audio problem: Helga rides past Arnold in a bus and yells "24 hours until you die!" or something like that. Her mouth never moves- it just stays open in an evil smile.
Suggested correction: Although it's hard to make out, her mouth is moving when she says that. Also, she says "23 hours until you die!" not 24.