Other mistake: In the closed-captioning, when Arnold and Gerald "touch thumbs" (and you hear that "sproing" sound), the caption says "[glass shatters]"
The Little Pink Book/Field Trip - S1-E2
Other mistake: When Arnold is reading the diary at the school the other kids ask him to read more. He says "OK, but it is the last page." There are more pages. When he starts to read, then it is the last page.
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)
Benchwarmer / Cool Jerk - S1-E11
Other mistake: The names for the Green and Yellow teams' players are the same.
Arnold Saves Sid / Hookey - S2-E7
Other 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.
The High Life / Best Friends - S2-E10
Other mistake: Best Friends: When Arnold walks across the table during the fashion show, a small chunk of the spotlight vanishes mid-shot. (00:22:13)
The High Life / Best Friends - S2-E10
Other mistake: Best Friends: When Gerald is first revealed during the fashion show, the curtains are transparent. They are never transparent in any other shot. (00:22:26)
Helga's Boyfriend / Crush on Teacher - S2-E14
Other mistake: Crush on Teacher: When the kids are playing baseball and the baseball hits Arnold, as he says, "I'm fine, Miss Felter," his eyelids are not colored in. (00:13:02)
Helga's Boyfriend / Crush on Teacher - S2-E14
Other mistake: Crush on Teacher: When Arnold and Gerald are walking to school and Arnold gets distracted by the birds and flowers, as he says, "Look at the flowers," his eyelids are not colored in. (00:14:37)
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.
Runaway Float / Partners - S2-E20
Other mistake: Runaway Float: After Nick Vermicelli says that the parade float is a total mess, as Arnold says, "It's not a mess," the background is of the school hallway, not Arnold's garage. (00:05:28)
Runaway Float / Partners - S2-E20
Other mistake: Runaway Float: After Bob says, "Now this float has to scream 'beeper' at the top of its lungs!", as he walks away from Arnold and Helga, Joey has white skin, blonde hair, and an orange shirt. (00:06:31)
Runaway Float / Partners - S2-E20
Other mistake: Runaway Float: When Arnold tears apart the big beeper on the parade float, the float's platform is missing, which makes it look like Bob and Nick are on the road. This happens again after Arnold stops the float, which makes it look like Bob and Nick are floating as a result. (00:10:19)
Arnold's Room / Helga vs. Big Patty - S3-E4
Other mistake: Helga vs. Big Patty: When Helga dreams about boxing Patty, as she steps back from her, she is standing in mid-air for about a second. (00:17:00)
The Aptitude Test / Oskar Gets a Job - S3-E9
Other mistake: Oskar Gets a Job: In the beginning of the episode, Arnold and Gerald overhear Oskar arguing with a man in his room. In the close-up of Arnold and Gerald as Oskar says, "You're a big man, aren't you?", Arnold's right eyelid is not colored in. (00:12:17)
The Aptitude Test / Oskar Gets a Job - S3-E9
Other mistake: Oskar Gets a Job: On the second day that Oskar forgets to do his job, Arnold reminds him that he has newspapers to deliver. After Oskar says, "You won't believe what happened," Arnold blinks, and his right eyelid is not colored in. (00:18:56)
Career Day / Hey Harold! - S3-E11
Other mistake: Hey Harold!: When Harold and Patty are dancing together, as Harold says, "They said I didn't apply myself," Patty blinks twice, and her right eyelid is not colored in. (00:17:00)
Career Day / Hey Harold! - S3-E11
Other mistake: Hey Harold!: When Harold's family is talking about Patty during dinner, as Harold's mother says, "We can show her those adorable baby pictures of you," her left eyelid is not colored in. (00:20:39)
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 & Lila / Grand Prix - S3-E13
Other mistake: Arnold and Lila: When Rhonda, Lila and Nadine are talking about what Helga wrote on the wall, as Lila says, "It couldn't possibly be true, could it?", she blinks, and her right eyelid is not coloured in. (00:03:12)