Longest Monday / Eugene's Pet - S2-E4
Continuity mistake: In "Longest Monday" at one point in the episode, Arnold and Gerald run off of a bus and down an alley. Two fifth graders come chasing after them. In the next scene, you see Arnold and Gerald hiding in the sewer under the 5th graders. Arnold then crawls through a very narrow tube, and Gerald follows. You then see the end of the tube and Gerald come out of the it first, and Arnold climbs out last. It would be impossible for Arnold and Gerald to switch places inside the tube because it was way too narrow.

Mud Bowl / Gerald Moves Out - S2-E9
Continuity mistake: When Gerald catches his little sister destroying his cassette tape, the book she is wrapping changes color from blue to green. (00:12:30)
Continuity mistake: When Lila is finishing her first joke, Rhonda suddenly switches from her French outfit to her "usual" one; also, during the Jell-O incident, her beret disappears and then reappears.
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: The kids' teacher in "Teachers Strike" is Miss Slovak, who was their teacher in the first season, but in the first episode of this season they had a new teacher, Mr. Simmons.
Suggested correction: Other than the few episodes that take place during a specific time of year; these episodes are not meant to be taken in chronological order. Just roughly in the same 4th grade school year.
Arnold Saves Sid / Hookey - S2-E7
Continuity mistake: The kids' teacher in this episode is Miss Slovak, who was their teacher in the first season, but in the first episode of this season they have a new teacher, Mr. Simmons.
Suggested correction: Other than the few episodes that take place during a specific time of year; these episodes are not meant to be taken in chronological order. Just roughly in the same 4th grade school year.
Arnold Saves Sid / Hookey - S2-E7
Continuity mistake: The clock in the police station looks like it says it's after 5:00, but school is in session.
Steely Phil / Quantity Time - S2-E12
Continuity mistake: The digits on Arnold's clock get bigger and change shape while he's talking to Grandpa.

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.
Save The Tree / New Teacher - S2-E1
Continuity mistake: In the beginning of 'Save The Tree', the tree ladder is a distance above the ground. Later on in the episode, when Arnold and his friends go to the tree house for the last time, the ladder is practically touching the ground.
Save The Tree / New Teacher - S2-E1
Continuity mistake: When Harold eats Mr. Simmons' tomato sandwich, there is a red stain from the tomato on Harold's desk. This stain disappears in later shots.
Runaway Float / Partners - S2-E20
Continuity mistake: The kids' teacher in this episode is Miss Slovak, who was their teacher in the first season, but in the first episode of this season they had a new teacher, Mr. Simmons.
Suggested correction: Other than the few episodes that take place at a specific time; this series was not meant to be taken in chronological order. Just roughly during the same 4th grade school year.
Part-Time Friends / Bio Square - S2-E19
Continuity mistake: The kids' teacher in "Bio Square" is Miss Slovak, who was their teacher in the first season, but in the first episode of this season they had a new teacher, Mr. Simmons.
Suggested correction: Other than the few episodes that take place at a specific time; this series is not meant to be taken in chronological order. Just roughly during the same 4th grade school year.

Coach Wittenberg / Four-Eyed Jack - S2-E16
Factual error: When the kids are bowling for the first time, the placement of the pins is wrong, and when Arnold is bowling there are 11 pins.
Save The Tree / New Teacher - S2-E1
Continuity mistake: In New Teacher when the principal is telling the class about their new teacher the students switch seats between shots.
Steely Phil / Quantity Time - S2-E12
Continuity mistake: Chinese Checkers is supposed to be with ten pieces per side, not six.
Arnold Saves Sid / Hookey - S2-E7
Revealing mistake: Arnold and Gerald's lockers don't have padlocks, like most of the others do.

Freeze Frame / Phoebe Cheats - S2-E8
Continuity mistake: The next night, Phoebe's bed clothes switch back and forth between her nightgown and her dress.

Eating Contest / Rhonda's Glasses - S2-E13
Continuity mistake: In the last scene, Rhonda is seen through the bus's rear window as sitting in the back of the bus - but just before that, she's talking to the girl with the frizzy hair in a seat closer to the front.