When Arthur and his soon-to-be classmates scream to find out they've been sorted into Mr. Ratburn's class, when the same scene continues after the title card, the background shows them being in the library until in the next few seconds, they're back in the hallway where they should be.
On Arthur and his classmates' first day of school in Mr. Ratburn's class, when Mr. Ratburn hands out papers to his students, he is standing several feet away from the desks while passing them out. It would not be possible unless he was actually within a few feet from each of the desks.
The librarian Ms. Turner first appears in this episode, but only for a few seconds of screen time. She is colored differently than in later episodes she appears in.
In "Arthur's Spelling Trubble", the Brain is shown not to like homework; yet in all other episodes, due to his superior intelligence, he he has no problems with it.
If the Brain is intelligent (hence his nickname he goes by) and that he and Arthur were selected to participate in the Spellathon due being the only students to pass the spelling bee in Mr. Ratburn's class, shouldn't he be able to survive through the Spellathon and be the last to be eliminated (instead of Prunella whom won the previous year's Spellathon) instead of being the first to be eliminated? It seems as if he intentionally misspelled the word "fear" as F-E-R-E.