At the beginning of "Locked in the Library," Prunella can be seen in Mr. Ratburn's 3rd grade class. According to several other episodes, Prunella is in the 4th grade, so she shouldn't have been in the class.
In Arthur's Pet Business, D.W.'s naked butt cheeks can be seen briefly when she is running out of the bathtub yelling for help (her towel flaps up near the back of her.)
Watch Perky's puppies in "Arthur's Pet Business." There's a palette shift in which two of them are a different color of yellow than the other and then when the angle changes for a second, they're all the same color.
When D.W. and Arthur are fighting over the remote control in "D.W. the Copycat," time seems to freeze on their respective shows: The Mary Moo-Cow Show and The Bionic Bunny Show. Proof-positive that if nobody is watching, nothing happens.
"Arthur's Lost Library Book" seems to have "chapters" in the episode. They are indicated by D.W. wearing monster gloves and amplifying her voice with a cardboard tube. The chapters include "Chapter 1: Arthur Goes to the Library," "Chapter 2: One Week Later," "Chapter 3: The Investigation," and "Chapter 4: It's Lost, OK? Face It, You Lost It."
These stories mark the first appearances of Nadine (D.W's invisible friend), Ms. Turner (the librarian) and the Scare-Your-Pants-Off book series (a parody of the Goosebumps books.)
Arthur appears shirtless for the first time.
When D.W's mother says,"It's almost time for bed," there was a mistake. The next scene shows D.W in the bathtub so her mother should've said," It's almost time for your bath" or "it's almost bathtime."
In "Arthur and the Real Mr. Ratburn," Sue Ellen's hair keeps changing colors. In the vampire clip, her hair is black. In a scene in Mr. Ratburn's room, it's dark brown. Sue-Ellen will not be introduced until later this first season.
In "Spelling Trubble" when Mr. Ratburn is erasing the board not all of it is erased (some of the underline under "Bee" isn't erased) yet it still disappears in the chalk dust.
Regarding the goof about Buster's reading: the show apparently has no timeline. The kids are always shown as being in third grade, so the events of this episode could have taken place well after the events of the episode in which Buster said he had never read a whole book.
If I'm not mistaken, Buster says in "Arthur and the Real Mr. Ratburn" that he read a book where kids became detectives, but in "Buster Hits the Books," which doesn't occur until the next season, Buster says that he's never read a whole book.
When Arthur asks Francine why she can't play, the green bow is missing but in the next shot, the bow is back.
"Francine's Bad Hair Day"- When Prunella screams about Francine getting the ball, you can see Francine looking at Prunella.
"Francine's Bad Hair Day"- In Francine's dream when Arthur is holding the ball, he has no pupils.
When the teacher hands him his test paper, the paper just says Arthur's name and the rest of the paper is blank!
When Arthur comes out of the girl's bathroom when everyone is staring at him, you can see D.W. and Mrs. Woods(not introduced yet). Why are they there? They don't go to that school.
"Arthur's Eyes"- Muffy is in this episode and he gets his glasses, but in "Arthur and the True Francine" he already has his glasses and she moves in.
In "Arthur's Eyes", Arthur is seen without his glasses for most of the show. They appear to be fairly standard, white circles with black pupils. This also applies to the majority of the first season and earlier in the second season. But in later episodes when his glasses come off, they appear as tiny black dots (ala Prunella's eyes.)
In theme song, Arthur is seen walking around a globe of the Earth. Unfortunately, he walks over the Pacific Ocean. A special land mass had to be invented between the Americas and Asia to even out the look of the landmasses.
Editor's reply: It's a theme song animation! Anything can happen in it! Like how could Arthur jump through a brick wall? Theme song, people, theme song!