Hall Monitor / Harold's Bar Mitzvah - S2-E15
Other mistake: Hall Monitor: During detention, the class helps Phoebe realise how much she has changed. When Helga wipes the window so Phoebe can see her reflection, in the first shot, Phoebe's reflection is not backwards as it should be. (00:10:45)

Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Harold's Bar Mitzvah: In the beginning, when Stinky asks Harold if he wants to play stickball, there is no wristband on his arm. Harold says he has to go do his lessons, and in the next shot, a wristband appears on Stinky's arm, then disappears. Later on, when Harold comes out of the synagogue, his wristbands are back on his arms. (00:12:03)

Hall Monitor / Harold's Bar Mitzvah - S2-E15
Other mistake: In the credits, actor Elliott Gould's name is misspelled as "Elliot Gould." (00:22:59)

Hall Monitor / Harold's Bar Mitzvah - S2-E15
Other mistake: In the credits, Justin Shenkarow is credited twice for voicing Harold. (00:22:59)
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Hall monitor: During the school assembly, Principal Wartz's necktie has diagonal stripes, and its top knot stripes switch to the opposite direction, then revert to the proper direction.
Hall Monitor / Harold's Bar Mitzvah - S2-E15
Continuity mistake: Hall Monitor: While Helga is hall monitor, her watch repeatedly disappears and reappears on her wrist.
Coach Wittenberg / Four-Eyed Jack - S2-E16
Continuity mistake: Coach Wittenburg's anchor tattoo changes color from red to purple in between shots.
Suggested correction: No, his tattoo is always red.

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.
Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Arnold makes a boat out of a block of wood, there is a blue cup on the newspapers with gray scissors and another orange object in it. In the next shot, the cup becomes green, and the scissors and other object become pink. As the scene continues, they change colours a few more times. The pencils also become the same colour as the newspapers. (00:02:11 - 00:03:49)

Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Gerald puts the boat made out of the block of wood in the fish tank, the sail is pointing towards the right, but when the boat sinks, it's pointing towards the left. (00:02:18)

Tour de Pond / Teachers Strike - S2-E18
Other mistake: Tour de Pond: When Arnold, Gerald, and Grandpa are first shown at the Tour de Pond race, their ship is not sitting on the sidewalk, but rather on the edge of it, which makes it look like it’s floating in mid-air. (00:05:02)

Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Rex notices that Arnold's boat is winning and starts running, the red and yellow squares on his grandfather's badge change to red and black. (00:10:18)

Tour de Pond / Teachers Strike - S2-E18
Continuity mistake: Tour de Pond: When Rex's grandfather walks up to Arnold's Grandpa at the end, his badge has eight squares on it, but in the next shot, it changes to four stripes. (00:11:20)
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.
Suggested correction: I agree with the other correction, but it's also worth noting that in the production order, "Teacher's Strike" was made before "New Teacher" was. They were just aired out of order, just like many of the other episodes.

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.

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.

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
Revealing mistake: Runaway Float: When Arnold and Gerald are watching the parade, Arnold turns his head to look at the marching band. When he looks away from it, his left eye doesn't move, and it stays visible in his hair for the remainder of the shot. (00:07:51)

Runaway Float / Partners - S2-E20
Continuity mistake: Runaway Float: When Arnold first sees the beeper float, he says, "How can they control that thing?", and Gerald is sitting on the curb to the right of Arnold. In the next shot, Gerald is suddenly behind him. Arnold is also a lot further away from the curb than he originally was. (00:08:16)