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).
Continuity mistake: The first time you see the line of girls, Rhonda's shoes are "low-cut", but just before Helga says "Move it, football head", the shoes suddenly extend much higher (like they normally do in the stories).
Crabby Author / Rich Kid - S3-E17
Continuity mistake: In "Rich Kid" Lorenzo is introduced as a new student, but he was in a previous episode titled "Arnold's Room."
Suggested correction: Other than the few episodes where a specific time of year is taking place; these episodes are not meant to be taken to be shown in chronological order. Just roughly in the same 4th grade school year.
Best Man / Cool Party - S3-E12
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.
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.
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.
The Aptitude Test / Oskar Gets a Job - S3-E9
Plot hole: Mr. Simmons asked that each student put their name on the test folders, but the folders already had names on them when he handed them out.
Arnold's Thanksgiving - S3-E14
Continuity mistake: When Joey is shown in close-up, his missing tooth looks like it's there but it's covered with something black and his missing tooth keeps reappearing and disappearing in the last scenes.
Suggested correction: Joey never appears in this episode.
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.
Arnold Saves Sid / Hookey - S2-E7
Revealing mistake: Arnold and Gerald's lockers don't have padlocks, like most of the others do.
Suggested correction: Like you state, most of the other lockers have padlocks, which means that some don't. You can even see some lockers without padlocks in the beginning. This is not a reason as to why Arnold and Gerald's lockers having no padlocks is a mistake. It more has to do with the fact that their lockers in particular should have padlocks, because they usually have them in other appearances. Edit: While I do agree with what I said, I now think that changing the mistake's wording would have been a better option than adding a correction, as Arnold and Gerald's lockers not having padlocks is still a mistake on its own.
Monkeyman! / Buses, Bikes and Subways - S5-E1
Revealing mistake: Mr. Simmons counts 30 students in the bus, but nowhere near that many got off (nor have nearly that many fourth graders ever been shown).
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.
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.
Benchwarmer / Cool Jerk - S1-E11
Revealing mistake: The names for the Green and Yellow teams' players are the same.
Ghost Bride/Gearold VS Jameo - S5-E25
Continuity mistake: In the scene where they are running from the second ghost bride, they go into a crypt and close the doors. One of the kids puts a shovel through the handles to keep it shut. In the next shot, it's gone. In the shot after that it's back.
Beaned / Old Iron Man - S5-E11
Continuity mistake: When Arnold reads to Helga, the book title says "GEO-" and "GRAPHY" (two words); the next day, it says "GEOGRAPHY" (one word).
Stuck in a Tree / Rhonda Goes Broke - S5-E10
Revealing mistake: In the scene after the garbage dumpster scene, Buckley's lips disappear briefly while he's talking.