In one episode, Mr. Ratburn was shown to be overweight as a kid, before he began playing ping pong and lost weight. It's safe to assume his love of cake helped him gain weight in the first place.
Yeah, there are no fat people who eat balanced diets and no thin people who eat only junk. And kids never gain weight before having big growth spurts.
In the episode where Mr. Ratburn's class meets their doppelgangers, Arthur's is named Chester. It's a reference to President Chester A. Arthur.
Francine's overreactions to Arthur being mean to his sister make sense if you realize that she's the younger sister in the family and Catherine can be distant.
At first glance, the main title sequence with Brain dangling his feet in the pool doesn't seem to make sense since a season two episode established that Brain is pathologically afraid of water. However, his fear of water might explain why Brain then mistakes Mr. Ratburn for a shark and has such a frightened reaction.
In the episode "Meet Binky" the kids meet the Finnish band Binky who turn out to be holograms. We do see them in the background from time to time, meaning the holograms are based on real people.
The episode "Arthur's Lost Dog" is about Pal running off, trying to get a balloon for Baby Kate. It's an Early-Installment Weirdness for the future Pal and Kate episodes, since it doesn't include Animal Talk.
While Brain was definitely holding the Idiot Ball in "War of the Worms", his sudden belief in the giant worm invasion hoax set up by Fern and Binky actually makes sense due to a Call Back. He admitted in the early episode "Arthur's Big Sleepover" that the thing that scared him the most (at least at the time) was a film called Navy Versus The Nightcrawler-which was, of course, about a giant worm invading.
More Brain Brilliance: the season one episode "Arthur's Spelling Trubble" features a spelling bee in which Brain misspells the word fear. At first it seems like nerves caused him to misspell such an easy word, but he may have purposefully misspelled it to get off of the stage and out of the spotlight.
In "To Eat or not to Eat" the Big Boss bars were extremely addictive and toxic, meaning that the main ingredient was basically a recreational drug. Which means it most likely caused brain damage when it was eaten...and almost every kid in the school was addicted to them...
It's also rather horrific to imagine a bunch of elementary-school age CHILDREN going through the nightmare of withdrawals.
Possibly even worse, said bars were apparently toxic to the point that their creator ran rather than eat one. And radioactive. And, as stated before, hundreds of kids were eating them nonstop. And they are probably still being eaten by some. Dear Lord....
In the episode with the Riddle Quest Game Show, Arthur lost on purpose because he was afraid he would end up being on the show forever and have to change schools. The same thing might eventually happen to Charloette!