When Arthur is tossing and turning in bed he's not wearing his glasses. After his first dream sequence he's seen with his glasses on.
In Arthur's dream sequence, after Arthur's parents question him about the long chain being attached to the copy of "The Mysterious Hand" from the library and he answers that it's supposedly how he has to check out copies of library books, they disappear when the camera cuts to the hallway. They would not have had time to step aside from the door to his room for the time being.
In Arthur's dream sequence where a copy of "The Mysterious Hand" he's reading is chained on and yanked back into the library by Ms. Turner, when the camera cuts to the corridor in his house, his right foot is shown going underneath one of the walls. This is due to an animation error.
In "D.W.'s Imaginary Friend", when Arthur and Buster ride the Hurl-A-Whirl, Buster's ears are shown to go through the glass barrier while the car they're riding in is spinning.
In "D.W.'s Imaginary Friend", even though Baby Kate is absent from this episode, Mrs. Read is not shown to be pregnant; and it is unconfirmed whether or not if Arthur and his friends (except for Prunella who is a grade above them) are in 2nd or 3rd grade in this episode's setting. Baby Kate was born in the time of "Arthur's Baby" and "D.W.'s Baby" that are set during Arthur's 2nd grade, presumably around the 2nd quarter.